8 If, then, the Holy Spirit proceeds both from the Father and from the Son, why said the Son, “He proceeds from the Father”? Why, do you think, but just because it is to Him He is wont to attribute even that which is His own, of whom He Himself also is? Hence we have Him saying, “My doctrine is not mine, but His that sent me.” If, therefore, in such a passage we are to understand that as His doctrine, which nevertheless He declared not to be His own, but the Father's, how much more in that other passage are we to understand the Holy Spirit as proceeding from Himself, where His words, “He proceeds from the Father,” were uttered so as not to imply, He proceeds not from me? But from Him, of whom the Son has it that He is God (for He is God of God), He certainly has it that from Him also the Holy Spirit proceeds: and in this way the Holy Spirit has it of the Father Himself, that He should also proceed from the Son, even as He proceeds from the Father.
Source: Tractates on the Gospel of John (New Advent)