Consider the following premises. forall y_1: R(y_1) -> S(y_1). forall y_1: T_4(y_1) -> S(y_1). exists y_1: S(y_1) -> R(y_1). Can we infer exists y_1: T_4(y_1) -> R(y_1) from them? If possible, name the inference rules being used at each step.
 From exists y_1: S(y_1) -> R(y_1), forall y_1: R(y_1) -> S(y_1) we can infer exists y_1: S(y_1) <-> R(y_1) via existential biconditional introduction. From exists y_1: S(y_1) <-> R(y_1) we can infer exists y_1: S(y_1) -> R(y_1) via existential biconditional elimination. Finally, from forall y_1: T_4(y_1) -> S(y_1), exists y_1: S(y_1) -> R(y_1) we can infer exists y_1: T_4(y_1) -> R(y_1) via existential transitivity. Therefore, the answer is yes.