Consider the following premises. exists z: P(z) -> Q(z). forall z: ~Q(z). forall z: Q(z) -> P(z). Can we infer forall z: P(z) from them?
 From exists z: P(z) -> Q(z), forall z: Q(z) -> P(z) we can infer exists z: P(z) <-> Q(z). Finally, from exists z: P(z) <-> Q(z), forall z: ~Q(z) we can infer exists z: ~P(z), which contradicts forall z: P(z). Therefore, the answer is no.