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