 Kripke then defines a sentence \(A\) of the language of pure substitutional quantificational logic to be valid if, and only if \(A\) comes out true no matter what base language \(\mathcal{L}\) and non-empty class of terms \(\mathcal{C}\) we take as input for the substitutional expansion and what predicates of \(\mathcal{L}\) we substitute for the predicates of \(A\). In particular, Kripke notes that when the quantifiers of a valid sentence of pure quantificational logic are suitably rewritten as substitutional quantifiers, we obtain a valid sentence in the language of pure substitutional quantificational logic.