Consider the following premises. exists z_1: T_4(z_1) <-> S(z_1). forall z_1: T_4(z_1) -> S(z_1). Can we infer exists z_1: T_4(z_1) -> S(z_1) from them? If possible, name the inference rules being used at each step.
 From exists z_1: T_4(z_1) <-> S(z_1) we can infer exists z_1: S(z_1) -> T_4(z_1) via existential biconditional elimination. From exists z_1: S(z_1) -> T_4(z_1), forall z_1: T_4(z_1) -> S(z_1) we can infer exists z_1: S(z_1) <-> T_4(z_1) via existential biconditional introduction. Finally, from exists z_1: S(z_1) <-> T_4(z_1) we can infer exists z_1: T_4(z_1) -> S(z_1) via existential biconditional elimination. Therefore, the answer is yes.