Consider the following premises. forall x: W(x) <-> W_1(x). forall x: S_3(x) or W(x). forall x: ~S_3(x). Can we infer forall x: W_1(x) from them?
 From forall x: S_3(x) or W(x), forall x: ~S_3(x) we can infer forall x: W(x). From forall x: W(x) <-> W_1(x) we can infer forall x: W(x) -> W_1(x). Finally, from forall x: W(x) -> W_1(x), forall x: W(x) we can infer forall x: W_1(x). Therefore, the answer is yes.