Consider the following premises. forall y_1: P_2(y_1). forall y_1: T(y_1) <-> U(y_1). exists y_1: P_2(y_1) -> T(y_1). Can we infer exists y_1: T(y_1) from them?
 From forall y_1: T(y_1) <-> U(y_1) we can infer forall y_1: U(y_1) -> T(y_1). From forall y_1: P_2(y_1) we can infer forall y_1: P_2(y_1) or U(y_1). Finally, from exists y_1: P_2(y_1) -> T(y_1), forall y_1: U(y_1) -> T(y_1), forall y_1: P_2(y_1) or U(y_1) we can infer exists y_1: T(y_1). Therefore, the answer is yes.