29 Concerning the Holy Spirit I ought not to be silent, and yet I have no need to speak; still, for the sake of those who are in ignorance, I cannot refrain. There is no need to speak, because we are bound to confess Him, proceeding, as He does, from Father and Son. For my own part, I think it wrong to discuss the question of His existence. He does exist, inasmuch as He is given, received, retained; He is joined with Father and Son in our confession of the faith, and cannot be excluded from a true confession of Father and Son; take away a part, and the whole faith is marred.
If any man demand what meaning we attach to this conclusion, he, as well as we, has read the words of the Apostle, Because you are sons of God, God has sent the Spirit of His Son into our hearts, crying, Abba, Father, and Grieve not the Holy Spirit of God, in Whom you have been sealed, and again, But we have received not the spirit of this world, but the Spirit which is of God, that we may know the things that are given unto us by God, and also But you are not in the flesh but in the Spirit, if so be that the Spirit of God is in you.
But if any man has not the Spirit of Christ, he is not His, and further, But if the Spirit of Him that raised up Jesus from the dead dwells in you, He that raised up Christ from the dead shall quicken also your mortal bodies for the sake of His Spirit which dwells in you. Wherefore since He is, and is given, and is possessed, and is of God, let His traducers take refuge in silence. When they ask, Through Whom is He? To what end does He exist? Of what nature is He?
We answer that He it is through Whom all things exist, and from Whom are all things, and that He is the Spirit of God, God's gift to the faithful. If our answer displease them, their displeasure must also fall upon the Apostles and the Prophets, who spoke of Him exactly as we have spoken. And furthermore, Father and Son must incur the same displeasure.
Source: On the Trinity (New Advent)