Consider the following premises. forall y: S_3(y) or ~W_2(y). forall y: W_2(y) <-> S_3(y). Can we infer forall y: S_3(y) <-> W_2(y) from them?
 From forall y: S_3(y) or ~W_2(y) we can infer forall y: W_2(y) -> S_3(y). From forall y: W_2(y) <-> S_3(y) we can infer forall y: S_3(y) -> W_2(y). Finally, from forall y: S_3(y) -> W_2(y), forall y: W_2(y) -> S_3(y) we can infer forall y: S_3(y) <-> W_2(y). Therefore, the answer is yes.