Objection 1. It would seem that the persons cannot be predicated of the concrete essential names; so that we can say for instance, "God is three persons"; or "God is the Trinity." For it is false to say, "man is every man," because it cannot be verified as regards any particular subject. For neither Socrates, nor Plato, nor anyone else is every man. In the same way this proposition, "God is the Trinity," cannot be verified of any one of the "supposita" of the divine nature. For the Father is not the Trinity; nor is the Son; nor is the Holy Ghost. So to say, "God is the Trinity," is false.
Objection 2. Further, the lower is not predicated of the higher except by accidental predication; as when I say, "animal is man"; for it is accidental to animal to be man. But this name "God" as regards the three persons is as a general term to inferior terms, as Damascene says (De Fide Orth. iii, 4). Therefore it seems that the names of the persons cannot be predicated of this name "God," except in an accidental sense.
On the contrary, Augustine says, in his sermon on Faith [Serm. ii, in coena Domini], "We believe that one God is one divinely named Trinity."
I answer that, As above explained (5), although adjectival terms, whether personal or notional, cannot be predicated of the essence, nevertheless substantive terms can be so predicated, owing to the real identity of essence and person. The divine essence is not only really the same as one person, but it is really the same as the three persons. Whence, one person, and two, and three, can be predicated of the essence as if we were to say, "The essence is the Father, and the Son, and the Holy Ghost." And because this word "God" can of itself stand for the essence, as above explained (4, ad 3), hence, as it is true to say, "The essence is the three persons"; so likewise it is true to say, "God is the three persons."
Reply to Objection 1. As above explained this term "man" can of itself stand for person, whereas an adjunct is required for it to stand for the universal human nature. So it is false to say, "Man is every man"; because it cannot be verified of any particular human subject.
On the contrary, this word "God" can of itself be taken for the divine essence. So, although to say of any of the "supposita" of the divine nature, "God is the Trinity," is untrue, nevertheless it is true of the divine essence. This was denied by Porretanus because he did not take note of this distinction.
Reply to Objection 2. When we say, "God," or "the divine essence is the Father," the predication is one of identity, and not of the lower in regard to a higher species: because in God there is no universal and singular. Hence, as this proposition, "The Father is God" is of itself true, so this proposition "God is the Father" is true of itself, and by no means accidentally.
Source: Summa Theologica (New Advent)