Consider the following premises. forall z_3: T(z_3). forall z_3: R_2(z_3) <-> S_3(z_3). exists z_3: R_2(z_3). Can we infer exists z_3: S_3(z_3) and T(z_3) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R_2(z_3) <-> S_3(z_3) we can infer forall z_3: R_2(z_3) -> S_3(z_3) via universal biconditional elimination. From forall z_3: R_2(z_3) -> S_3(z_3), exists z_3: R_2(z_3) we can infer exists z_3: S_3(z_3) via existential modus ponens. Finally, from exists z_3: S_3(z_3), forall z_3: T(z_3) we can infer exists z_3: S_3(z_3) and T(z_3) via existential conjunction. Therefore, the answer is yes.