Consider the following premises. forall y: R(y) <-> P_2(y). exists y: R(y) <-> T(y). Can we infer exists y: T(y) -> P_2(y) from them?
 From exists y: R(y) <-> T(y) we can infer exists y: T(y) -> R(y). From forall y: R(y) <-> P_2(y) we can infer forall y: R(y) -> P_2(y). Finally, from exists y: T(y) -> R(y), forall y: R(y) -> P_2(y) we can infer exists y: T(y) -> P_2(y). Therefore, the answer is yes.