Yes. The Holy Ghost proceeds from the Son because it cannot be said that the Son and the Holy Ghost proceed from the Father in such a way as that neither of them proceeds from the other, unless we admit in them a material distinction, which is impossible.
If from the one Person of the Father, two persons proceed, the Son and the Holy Ghost, there must be some order between them. Nor can any other be assigned except the order of their nature, whereby one is from the other.
It must be said that the Holy Ghost is from the Son. For if He were not from Him, He could in no wise be personally distinguished from Him.
The order of the procession of each one agrees with this conclusion because the Son proceeds by the way of the intellect as Word, and the Holy Ghost by way of the will as Love.
Now love must proceed from a word. For we do not love anything unless we apprehend it by a mental conception. Hence also in this way it is manifest that the Holy Ghost proceeds from the Son.
The Word in God is not taken after the similitude of the vocal word, whence the breath [spiritus] does not proceed; for it would then be only metaphorical; but after the similitude of the mental word, whence proceeds love.
It cannot be said that the divine Persons are distinguished from each other in any absolute sense; for it would follow that there would not be one essence of the three persons: since everything that is spoken of God in an absolute sense, belongs to the unity of essence.
Therefore it must be said that the divine persons are distinguished from each other only by the relations. Now the relations cannot distinguish the persons except forasmuch as they are opposite relations; which appears from the fact that the Father has two relations, by one of which He is related to the Son, and by the other to the Holy Ghost; but these are not opposite relations, and therefore they do not make two persons, but belong only to the one person of the Father.
If therefore in the Son and the Holy Ghost there were two relations only, whereby each of them were related to the Father, these relations would not be opposite to each other, as neither would be the two relations whereby the Father is related to them. Hence, as the person of the Father is one, it would follow that the person of the Son and of the Holy Ghost would be one, having two relations opposed to the two relations of the Father. But this is heretical since it destroys the Faith in the Trinity.
Therefore the Son and the Holy Ghost must be related to each other by opposite relations. Now there cannot be in God any relations opposed to each other, except relations of origin. And opposite relations of origin are to be understood as of a "principle," and of what is "from the principle." Therefore we must conclude that it is necessary to say that either the Son is from the Holy Ghost; which no one says; or that the Holy Ghost is from the Son, as we confess.
The Holy Ghost is distinguished from the Son, inasmuch as the origin of one is distinguished from the origin of the other; but the difference itself of origin comes from the fact that the Son is only from the Father, whereas the Holy Ghost is from the Father and the Son -- for otherwise the processions would not be distinguished from each other.