Consider the following premises. forall x: Q(x) <-> P(x). forall x: ~P(x). forall x: P(x) <-> Q(x). Can we infer forall x: ~Q(x) from them?
 From forall x: P(x) <-> Q(x) we can infer forall x: Q(x) -> P(x). From forall x: Q(x) <-> P(x) we can infer forall x: P(x) -> Q(x). From forall x: P(x) -> Q(x), forall x: Q(x) -> P(x) we can infer forall x: P(x) <-> Q(x). Finally, from forall x: P(x) <-> Q(x), forall x: ~P(x) we can infer forall x: ~Q(x). Therefore, the answer is yes.