Logichard
0:00.0

In classical first-order logic, quantifiers can be shifted under certain conditions. For instance, if xx is not free in QQ, then x(P(x)    Q)    (xP(x)    Q)\forall x (P(x) \implies Q) \iff (\exists x P(x) \implies Q). However, this equivalence does not fully hold in Intuitionistic Predicate Logic. Which of the following quantifier shifts is classically valid but NOT intuitionistically valid?