Consider the following premises. forall y: T(y) <-> P_3(y). exists y: T(y) -> P_3(y). Can we infer exists y: P_3(y) -> T(y) from them?
 From forall y: T(y) <-> P_3(y) we can infer forall y: P_3(y) -> T(y). From exists y: T(y) -> P_3(y), forall y: P_3(y) -> T(y) we can infer exists y: T(y) <-> P_3(y). Finally, from exists y: T(y) <-> P_3(y) we can infer exists y: P_3(y) -> T(y). Therefore, the answer is yes.