Consider the following premises. exists y: P(y) <-> W(y). forall y: P(y) or ~T_4(y). Can we infer exists y: T_4(y) -> W(y) from them?
 From exists y: P(y) <-> W(y) we can infer exists y: P(y) -> W(y). From forall y: P(y) or ~T_4(y) we can infer forall y: T_4(y) -> P(y). Finally, from forall y: T_4(y) -> P(y), exists y: P(y) -> W(y) we can infer exists y: T_4(y) -> W(y). Therefore, the answer is yes.