Consider the following premises. forall x: T(x) <-> T_2(x). forall x: S(x) -> T_2(x). forall x: T(x) -> S(x). Can we infer forall x: T_2(x) -> T(x) from them?
 From forall x: T(x) -> S(x), forall x: S(x) -> T_2(x) we can infer forall x: T(x) -> T_2(x). Finally, from forall x: T(x) <-> T_2(x) we can infer forall x: T_2(x) -> T(x). Therefore, the answer is yes.