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