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