  The same example illustrates that the substitutivity principle for  predicates will have to fail in modal logic as well. For, according  to our example, the predicates ‘D’ and  ‘P’ that are true of John's dogs and of John's  pets, respectively, are coextensional, i.e.,  ∀x(Dx ↔ Px). However, while  substituting the latter predicate for the former in (3) results in a  sentence with the same truth value, the same substitution in (5) does not. 