Consider the following premises. forall x_1: Q(x_1) <-> T_2(x_1). exists x_1: T_2(x_1) -> Q(x_1). forall x_1: Q(x_1) -> T_2(x_1). Can we infer exists x_1: Q(x_1) -> T_2(x_1) from them?
 From forall x_1: Q(x_1) <-> T_2(x_1) we can infer forall x_1: T_2(x_1) -> Q(x_1). From exists x_1: T_2(x_1) -> Q(x_1), forall x_1: Q(x_1) -> T_2(x_1) we can infer exists x_1: T_2(x_1) <-> Q(x_1). Finally, from exists x_1: T_2(x_1) <-> Q(x_1) we can infer exists x_1: Q(x_1) -> T_2(x_1). Therefore, the answer is yes.