Consider the following premises. forall y: U(y) or ~U_1(y). forall y: W_2(y) <-> U(y). Can we infer forall y: U_1(y) -> W_2(y) from them?
 From forall y: W_2(y) <-> U(y) we can infer forall y: U(y) -> W_2(y). From forall y: U(y) or ~U_1(y) we can infer forall y: U_1(y) -> U(y). Finally, from forall y: U_1(y) -> U(y), forall y: U(y) -> W_2(y) we can infer forall y: U_1(y) -> W_2(y). Therefore, the answer is yes.