The Holy Spiritas regards His existenceproceeds (originates) eternally from the Father (St. Gregory Palamas [13th century], Philokalia), and not from the Son. To say that he proceeds from Them is to imply double origin.
The Apostle states:
"the Spirit of truth who proceeds from the Father, He will testify about Me." [St. John 15:26]
St. John of Damascus (8th century desert father) states:
Likewise we believe also in one Holy Spirit, the Lord and Giver of Life: Who proceedeth from the Father and resteth in the Son...proceeding from the Father and communicated through the Son.
(We believe) in one Father, the beginning, and cause of all: begotten of no one: without cause or generation, alone subsisting: creator of all: but Father of one only by nature, His Only-begotten Son and our Lord and God and Saviour Jesus Christ, and Producer of the most Holy Spirit. [Exact Exposition of the Orthodox Faith, Book I, Chapter VIII]
And I beheld, and, lo, in the midst of the throne and of the four beasts, and in the midst of the elders, stood a Lamb as it had been slain, having seven horns and seven eyes, which are the seven Spirits of God sent forth into all the earth. - Revelation 5:6