Consider the following premises. forall y: T_3(y) -> P(y). exists y: S_4(y) <-> T_3(y). Can we infer exists y: S_4(y) -> P(y) from them?
 From exists y: S_4(y) <-> T_3(y) we can infer exists y: S_4(y) -> T_3(y). Finally, from exists y: S_4(y) -> T_3(y), forall y: T_3(y) -> P(y) we can infer exists y: S_4(y) -> P(y). Therefore, the answer is yes.