Consider the following premises. forall y_2: T_1(y_2) <-> W(y_2). exists y_2: W(y_2) or ~T_1(y_2). Can we infer exists y_2: W(y_2) <-> T_1(y_2) from them?
 From exists y_2: W(y_2) or ~T_1(y_2) we can infer exists y_2: T_1(y_2) -> W(y_2). From forall y_2: T_1(y_2) <-> W(y_2) we can infer forall y_2: W(y_2) -> T_1(y_2). Finally, from forall y_2: W(y_2) -> T_1(y_2), exists y_2: T_1(y_2) -> W(y_2) we can infer exists y_2: W(y_2) <-> T_1(y_2). Therefore, the answer is yes.