In this (derived) proposition the predicate is supposed to be identified with the subject, that is, 'animal' is identified with 'man'. But how can this be? Isn't it true that the meanings of ' animal ' and ' man ' are, althoug similar, different? So how can they then be identified with each other?
Here we must invoke the theory of designation which is an amended version of the scholastic theory of supposition. Because it will later be treated in detail, we will be very succinct here.
The term ' man ' and the term ' animal ' each have their natural (intrinsic) meaning or signification. They refer to a certain nature present in certain things. Indeed, they are concepts. But as soon as these concepts enter into a proposition, their meaning can become restricted as a result of now figuring in a propositional context. Having their intrinsic signification, they designate certain existing individuals, where the total of these (designated) individuals is not necessarily equal to the full extension of the concept.
In the proposition ' man is an animal ' the full extension of the concept ' man ' is not restricted, because the predicate ' animal ' does not impose any limitation on this extension. So the actual meaning of the term ' man ' as used in this proposition refers to all individual men. The intrinsic meaning of the term ' animal ' refers to all animals (of which all men form a subgroup). On the other hand, the actual meaning of the term ' animal ' as used in that proposition is restricted by the term ' man ', and so refers only to all individual animals that are men. And now we see that although the terms ' man ' and ' animal ' signify different formal contents (they are similar, but nevertheless different), they, in the proposition designate the same, and can thus be identified.