7 And for no other reason, I suppose, is He called in a peculiar way the Spirit; since though asked concerning each person in His turn, we cannot but admit that the Father and the Son are each of them a Spirit; for God is a Spirit, that is, God is not carnal, but spiritual. By the name, therefore, which they each also hold in common, it was requisite that He should be distinctly called, who is not the one nor the other of them, but in whom what is common to both becomes apparent.
Why, then, should we not believe that the Holy Spirit proceeds also from the Son, seeing that He is likewise the Spirit of the Son? For did He not so proceed, He could not, when showing Himself to His disciples after the resurrection, have breathed upon them, and said, “Receive the Holy Spirit.” For what else was signified by such a breathing upon them, but that from Him also the Holy Spirit proceeds? And of the same character also are His words regarding the woman that suffered from the bloody flux: “Some one has touched me; for I perceive that virtue is gone out of me.” For that the Holy Spirit is also designated by the name of virtue, is both clear from the passage where the angel, in reply to Mary's question, “How shall this be, seeing I know not a man?” said, “The Holy Ghost shall come upon you, and the power [virtue] of the highest shall overshadow you;” and our Lord Himself when giving His disciples the promise of the Spirit, said, “But tarry ye in the city, until ye be endued with power [virtue] from on high;” and on another occasion, “You shall receive the power [virtue] of the Holy Ghost coming upon you, and you shall be witnesses unto me.” It is of this virtue that we are to believe, that the evangelist says, “Virtue went out of Him, and healed them all.”
Source: Tractates on the Gospel of John (New Advent)