Objection 1. It seems that the true and being are not convertible terms. For the true resides properly in the intellect, as stated (1); but being is properly in things. Therefore they are not convertible.
Objection 2. Further, that which extends to being and not-being is not convertible with being. But the true extends to being and not-being; for it is true that what is, is; and that what is not, is not. Therefore the true and being are not convertible.
Objection 3. Further, things which stand to each other in order of priority and posteriority seem not to be convertible. But the true appears to be prior to being; for being is not understood except under the aspect of the true. Therefore it seems they are not convertible.
On the contrary, the Philosopher says (Metaph. ii) that there is the same disposition of things in being and in truth.
I answer that, As good has the nature of what is desirable, so truth is related to knowledge. Now everything, in as far as it has being, so far is it knowable. Wherefore it is said in De Anima iii that "the soul is in some manner all things," through the senses and the intellect. And therefore, as good is convertible with being, so is the true. But as good adds to being the notion of desirable, so the true adds relation to the intellect.
Reply to Objection 1. The true resides in things and in the intellect, as said before (1). But the true that is in things is convertible with being as to substance; while the true that is in the intellect is convertible with being, as the manifestation with the manifested; for this belongs to the nature of truth, as has been said already (1). It may, however, be said that being also is in the things and in the intellect, as is the true; although truth is primarily in things; and this is so because truth and being differ in idea.
Reply to Objection 2. Not-being has nothing in itself whereby it can be known; yet it is known in so far as the intellect renders it knowable. Hence the true is based on being, inasmuch as not-being is a kind of logical being, apprehended, that is, by reason.
Reply to Objection 3. When it is said that being cannot be apprehended except under the notion of the true, this can be understood in two ways. In the one way so as to mean that being is not apprehended, unless the idea of the true follows apprehension of being; and this is true. In the other way, so as to mean that being cannot be apprehended unless the idea of the true be apprehended also; and this is false. But the true cannot be apprehended unless the idea of being be apprehended also; since being is included in the idea of the true. The case is the same if we compare the intelligible object with being. For being cannot be understood, unless being is intelligible. Yet being can be understood while its intelligibility is not understood. Similarly, being when understood is true, yet the true is not understood by understanding being.
Source: Summa Theologica (New Advent)