Steve Ray has a list of more than 35 loaded Questions for "Bible Christians" (quotation marks his)(link to the whole list). I originally planned to respond to just 35 of them, but the series seems to have been of interest, so in this extension, I'm responding to three more numbered questions in his list, plus fourteen "bonus questions" that take the form "Where does the Bible say ... ." I'm trying to provide the answers in the same common format as the original series, for easy reference. This is number 13/17.
Where does the Bible . . .
. . . tell us the Holy Spirit is one of the three Persons of the Trinity?
1) As discussed in a previous segment, the Scriptures don't use the word "Trinity."
2) The Scriptures, therefore, also don't use the precise terminology "person of the Trinity."
3) However, the identity of the Holy Spirit as God (i.e. as one of the three persons of the Trinity) is confirmed by a vast number of verses, such as the following:
Psalm 51:11 Cast me not away from thy presence; and take not thy holy spirit from me.
Notice that the Holy Spirit is equated with God's presence. This shows us, fairly simply, that the Holy Spirit is not merely an angel or the like, since to be with a mere angel would not be to be in God's presence.
There are many treatises that examine this important Scriptural doctrine in much greater depth. I've tried to give a simple and concise answer, but many writers from ancient times down to modern times, have given much greater and more comprehensive exegeses of Scripture to thoroughly demonstrate this same truth.