Consider the following premises. forall y: T_2(y) -> P(y). forall y: Q(y) -> R_4(y). exists y: P(y) -> Q(y). forall y: R_4(y) -> T_2(y). Can we infer exists y: R_4(y) -> T_2(y) from them?
 From forall y: T_2(y) -> P(y), exists y: P(y) -> Q(y) we can infer exists y: T_2(y) -> Q(y). From exists y: T_2(y) -> Q(y), forall y: Q(y) -> R_4(y) we can infer exists y: T_2(y) -> R_4(y). From forall y: R_4(y) -> T_2(y), exists y: T_2(y) -> R_4(y) we can infer exists y: R_4(y) <-> T_2(y). Finally, from exists y: R_4(y) <-> T_2(y) we can infer exists y: R_4(y) -> T_2(y). Therefore, the answer is yes.