Where the symbol formula_28 stands for the formula formula_1 with the term formula_24 substituted for formula_15. (See Substitution of variables.) In informal terms, this example allows us to state that, if we know that a certain property formula_32 holds for every formula_15 and that formula_24 stands for a particular object in our structure, then we should be able to claim formula_35. Again, "we are claiming that the formula" formula_36 "is valid", that is, we must be able to give a "proof" of this fact, or more properly speaking, a "metaproof". These examples are "metatheorems" of our theory of mathematical logic since we are dealing with the very concept of "proof" itself. Aside from this, we can also have Existential Generalization: