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