As he is by nature the proper Spirit of the Son, existing in him and coming forth through him, so he is proper to the Father; and if the Spirit is common to them, surely the other aspects of their substance will not be divided. And let not the habitually impious use the arguments of ignorance to lead us toward what it would be wrong for us even to think: that the Son is playing some subordinate role when he supplies creation with the Spirit who comes from the Father -- for some, in their ignorance, have not been afraid to say even this! The consistent thing, rather, is to believe that it is because [the Spirit] is proper to him, as of course he also is to God the Father, that [the Son] sends him on his holy disciples for their sanctification.
Cyril of Alexandria, In Jo. 15:26-27 (Pusey vol. 2 p. 607); qtd in Brian E. Daley, SJ, "The Fullness of the Saving God: Cyril of Alexandria on the Holy Spirit," The Theology of St. Cyril of Alexandria: A Critical Appreciation, Weinandy and Keating, eds. T & T Clark (New York: 2003) p. 135. In the first sentence, 'existing' translates huparchon and 'coming forth' translates proion. What is interesting here, however, is the importance placed on the community of the Spirit for recognizing the unity of the Trinity. Cyril actually seems to do this quite a bit; it seems to be an important aspect of his teaching on the Trinity.
