The letter does talk about "the doctrines of the Catholic Church" (meaning the universal church, not today's RCC) and "the sound Catholic Faith" (at the beginning and end of the letter). How are these doctrines and this faith defined, though? The constant appeal is to Scripture. We will see that in each of the sections.
First, section 1:
1. As there is one body of the Catholic Church, and a command is given us in the sacred Scriptures to preserve the bond of unity and peace, it is agreeable thereto that we should write and signify to one another whatever is done by each of us individually; so that whether one member suffer or rejoice, we may either suffer or rejoice with one another. Now there are gone forth in this diocese, at this time, certain lawless men, enemies of Christ, teaching an apostasy, which one may justly suspect and designate as a forerunner of Antichrist. I was desirous to pass such a matter by without notice, in the hope that perhaps the evil would spend itself among its supporters, and not extend to other places to defile the ears of the simple. But seeing that Eusebius, now of Nicomedia, who thinks that the government of the Church rests with him, because retribution has not come upon him for his desertion of Berytus, when he had cast an eye of desire on the Church of the Nicomedians, begins to support these apostates, and has taken upon him to write letters every where in their behalf, if by any means he may draw in certain ignorant persons to this most base and antichristian heresy; I am therefore constrained, knowing what is written in the law, no longer to hold my peace, but to make it known to you all; that you may understand who the apostates are, and the cavils which their heresy has adopted, and that, should Eusebius write to you, you may pay no attention to him, for he now desires by means of these men to exhibit anew his old malevolence, which has so long been concealed, pretending to write in their favour, while in truth it clearly appears, that he does it to forward his own interests.Notice that Alexander begins his comments with a reference to Scripture, specifically Ephesians 4:3-4 "Endeavouring to keep the unity of the Spirit in the bond of peace. There is one body, and one Spirit, even as ye are called in one hope of your calling ... ." Next he alludes to 1 Corinthians 12:26 "And whether one member suffer, all the members suffer with it; or one member be honoured, all the members rejoice with it." He then seems to allude to 1 John 2 "18 Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time. ... 22 Who is a liar but he that denieth that Jesus is the Christ? He is antichrist, that denieth the Father and the Son." and Jude 4 "For there are certain men crept in unawares, who were before of old ordained to this condemnation, ungodly men, turning the grace of our God into lasciviousness, and denying the only Lord God, and our Lord Jesus Christ." There is an interesting comment made by Alexander: "I am therefore constrained, knowing what is written in the law, no longer to hold my peace, but to make it known to you all ... ." What law can he be referring to? As an examination of the rest of the letter shows, it seems the law he has in mind is Scripture.
Turning to section 2:
2. Now those who became apostates are these, Arius, Achilles, Aeithales, Carpones, another Arius, and Sarmates, sometime Presbyters: Euzoïus, Lucius, Julius, Menas, Helladius, and Gaius, sometime Deacons: and with them Secundus and Theonas, sometime called Bishops. And the novelties they have invented and put forth contrary to the Scriptures are these following:—God was not always a Father, but there was a time when God was not a Father. The Word of God was not always, but originated from things that were not; for God that is, has made him that was not, of that which was not; wherefore there was a time when He was not; for the Son is a creature and a work. Neither is He like in essence to the Father; neither is He the true and natural Word of the Father; neither is He His true Wisdom; but He is one of the things made and created, and is called the Word and Wisdom by an abuse of terms, since He Himself originated by the proper Word of God, and by the Wisdom that is in God, by which God has made not only all other things but Him also. Wherefore He is by nature subject to change and variation as are all rational creatures. And the Word is foreign from the essence of the Father, and is alien and separated therefrom. And the Father cannot be described by the Son, for the Word does not know the Father perfectly and accurately, neither can He see Him perfectly. Moreover, the Son knows not His own essence as it really is; for He is made for us, that God might create us by Him, as by an instrument; and He would not have existed, had not God wished to create us. Accordingly, when some one asked them, whether the Word of God can possibly change as the devil changed, they were not afraid to say that He can; for being something made and created, His nature is subject to change.Notice that the standard Alexander immediately adopts is Scripture: "the novelties they have invented and put forth contrary to the Scriptures." Of course, as the rest of his comments are a short summary of the abominable heresies, he has no Scriptural support for these novelties.
Turning to section 3:
3. Now when Arius and his fellows made these assertions, and shamelessly avowed them, we being assembled with the Bishops of Egypt and Libya, nearly a hundred in number, anathematized both them and their followers. But Eusebius and his fellows admitted them to communion, being desirous to mingle falsehood with the truth, and impiety with piety. But they will not be able to do so, for the truth must prevail; neither is there any “communion of light with darkness,” nor any “concord of Christ with Belial.” For who ever heard such assertions before? or who that hears them now is not astonished and does not stop his ears lest they should be defiled with such language? Who that has heard the words of John, “In the beginning was the Word,” will not denounce the saying of these men, that “there was a time when He was not?” Or who that has heard in the Gospel, “the Only-begotten Son,” and “by Him were all things made,” will not detest their declaration that He is “one of the things that were made.” For how can He be one of those things which were made by Himself? or how can He be the Only-begotten, when, according to them, He is counted as one among the rest, since He is Himself a creature and a work? And how can He be “made of things that were not,” when the Father saith, “My heart hath uttered a good Word,” and “Out of the womb I have begotten Thee before the morning star?” Or again, how is He “unlike in substance to the Father,” seeing He is the perfect “image” and “brightness” of the Father, and that He saith, “He that hath seen Me hath seen the Father?” And if the Son is the “Word” and “Wisdom” of God, how was there “a time when He was not?” It is the same as if they should say that God was once without Word and without Wisdom. And how is He “subject to change and variation,” Who says, by Himself, “I am in the Father, and the Father in Me,” and “I and the Father are One;” and by the Prophet, “Behold Me, for I am, and I change not?” For although one may refer this expression to the Father, yet it may now be more aptly spoken of the Word, viz., that though He has been made man, He has not changed; but as the Apostle has said, “Jesus Christ is the same yesterday, to-day, and for ever.” And who can have persuaded them to say, that He was made for us, whereas Paul writes, “for Whom are all things, and by Whom are all things?”Alexander begins by mentioning a regional council in Africa. He notes, however, that not everyone accepted the anathema of that council, focusing primarily on Eusebius of Nicomedia.
Alexander argues that Eusebius of Nicomedia is wrong to have communion with Arius, citing 2 Corinthians 5:14-15 "Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness? And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?"
To rebut Arius' position, Alexander turns directly to Scripture, quoting from John 1:1: "In the beginning was the Word." He then also cites "only-begotten son" (John 1:18) and "all things were made by Him" (John 1:3).
He does not limit himself to the New Testament. He cites Psalm (LXX 44:2) "my heart has uttered a good word; I speak my works to the king." (See Psalm 45:1 in our Bibles) (Origen a spiritual ancestor of Athanasius in Alexandria (ca. 185 - 254), in his commentary on John, Book 1, at sections 151 and 280, pp. 64 and 91, draws the same connection to this psalm, which otherwise might not seem necessarily relevant.) He also cites Psalm (LXX 109:3) "Before the morning star have I begotten thee from the womb" (See Psalm 110:3 in our Bibles) (a younger contemporary of Athanasius, Epiphanius of Salamis (ca. 310 or 320 to 403) in his Panarion makes a similar connection to this Psalm, in Anacephalaeosis V, 65 "Against Paul the Samosatian," at 4,4-8, pp. 219-220)
He then goes back and cites Hebrews 1:3 "Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, ... " and John 14:9 "... he that hath seen me hath seen the Father ... ."
Alexander continues by citing the Biblical titles of "Word" (e.g. John 1:1) and "Wisdom" (e.g. 1 Corinthians 1:24, 30).
Alexander also cites John 14:10 "I am in the Father, and the Father in me" and John 10:30 "I and my Father are one."
Once again, Alexander goes back to the Old Testament and quotes Malachi 3:6: "For I am the Lord, I change not" (the "behold me" in Alexander's citation may be taken from Isaiah 65:1: "I am sought of them that asked not for me; I am found of them that sought me not: I said, Behold me, behold me, unto a nation that was not called by my name." or possibly from Malach 3:1: "Behold, I send forth my messenger, and he shall survey the way before me ...")
He then quotes from Hebrews 13:8: "Jesus Christ the same yesterday, and to day, and for ever" and again from Hebrews 2:10: "For it became him, for whom are all things, and by whom are all things, in bringing many sons unto glory, to make the captain of their salvation perfect through sufferings."
Turning to section 4:
4. As to their blasphemous position that “the Son knows not the Father perfectly,” we ought not to wonder at it; for having once set themselves to fight against Christ, they contradict even His express words, since He says, “As the Father knoweth Me, even so know I the Father.” Now if the Father knows the Son but in part, then it is evident that the Son does not know the Father perfectly; but if it is not lawful to say this, but the Father does know the Son perfectly, then it is evident that as the Father knows His own Word, so also the Word knows His own Father Whose Word He is.Notice again that Alexander quotes from Scripture, John 10:15 "As the Father knoweth me, even so know I the Father: ... ."
Turning to section 5:
5. By these arguments and references to the sacred Scriptures we frequently overthrew them; but they changed like chameleons, and again shifted their ground, striving to bring upon themselves that sentence, “when the wicked falleth into the depth of evils, he despiseth.” There have been many heresies before them, which, venturing further than they ought, have fallen into folly; but these men by endeavouring in all their cavils to overthrow the Divinity of the Word, have justified the other in comparison of themselves, as approaching nearer to Antichrist. Wherefore they have been excommunicated and anathematized by the Church. We grieve for their destruction, and especially because, having once been instructed in the doctrines of the Church, they have now sprung away. Yet we are not greatly surprised, for Hymenæus and Philetus did the same, and before them Judas, who followed the Saviour, but afterwards became a traitor and an apostate. And concerning these same persons, we have not been left without instruction; for our Lord has forewarned us; “Take heed lest any man deceive you: for many shall come in My name, saying, I am Christ, and the time draweth near, and they shall deceive many: go ye not after them;” while Paul, who was taught these things by our Saviour, wrote that “in the latter times some shall depart from the sound faith, giving heed to seducing spirits and doctrines of devils, which reject the truth.”Here Alexander makes it explicit that his constant and continual practice in rebutting these heresies was appeal to Scripture:"By these arguments and references to the sacred Scriptures we frequently overthrew them ... ." In condemning them as wicked he again quotes from the Old Testament Scriptures, Proverbs (LXX - Brenton trans.) 18:3: "When an ungodly man comes into a depth of evils, he despises them; but dishonour and reproach come upon him."
Finally, Alexander comes back to mentioning the church. He says that in view of their folly/heresies "Wherefore they have been excommunicated and anathematized by the Church."
He says that their apostasy is sad but not unexpected, citing Biblical examples of Hymenaeus and Philetus (2 Timothy 2:17-18) as well as Judas (e.g. Acts 1:25). He then points to Jesus' warning in Luke 21:8: "Take heed that ye be not deceived: for many shall come in my name, saying, I am Christ; and the time draweth near: go ye not therefore after them" and Paul's warning in 1 Timothy 4:1-2 " Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils; speaking lies in hypocrisy; having their conscience seared with a hot iron;"
Lastly, turning to section 6:
6. Since then our Lord and Saviour Jesus Christ has instructed us by His own mouth, and also hath signified to us by the Apostle concerning such men, we accordingly being personal witnesses of their impiety, have anathematized, as we said, all such, and declared them to be alien from the Catholic Faith and Church. And we have made this known to your piety, dearly beloved and most honoured fellow-ministers, in order that should any of them have the boldness to come unto you, you may not receive them, nor comply with the desire of Eusebius, or any other person writing in their behalf. For it becomes us who are Christians to turn away from all who speak or think any thing against Christ, as being enemies of God, and destroyers of souls; and not even to “bid such God speed,” lest we become partakers of their sins, as the blessed John hath charged us. Salute the brethren that are with you. They that are with me salute you.Notice again that Alexander appeals to the authority of Scripture as being the mouth of Jesus and the Apostles, referring to the warnings of section 5. There is again a reference to church discipline, but notice that Alexander is only asserting a declaration of what has been discovered, not assertion the ability to define what is true. Finally, he concludes with yet another warning from Scripture, 2 John 10-11: "If there come any unto you, and bring not this doctrine, receive him not into your house, neither bid him God speed: For he that biddeth him God speed is partaker of his evil deeds."
In conclusion, we see that Alexander of Alexandria, and possibly his right hand man Athanasius, both relied in this letter exclusively, explicitly, and extensively on the authority of Scripture to combat the Arian heresy. This letter, therefore, may not have any explicit assertion of Sola Scriptura, but it is a great example of Sola Scriptura in practice even in a ecclesiastical setting that is different from our own. A lot of the orthodox men of the church in that time endorsed this letter, which implicitly endorses the approach of Sola Scriptura. Amongst them were Athanasius, as Alexander introduces the letter by saying "Alexander, being assembled with his beloved brethren, the Presbyters and Deacons of Alexandria," which would have included Athanasius.