Consider the following premises. forall z: W(z) -> S_3(z). exists z: S(z) -> W(z). forall z: S_3(z) -> T_2(z). forall z: S_3(z) -> W(z). Can we infer exists z: S(z) -> T_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: S_3(z) -> W(z), forall z: W(z) -> S_3(z) we can infer forall z: S_3(z) <-> W(z) via universal biconditional introduction. From forall z: S_3(z) <-> W(z) we can infer forall z: W(z) -> S_3(z) via universal biconditional elimination. From forall z: W(z) -> S_3(z), forall z: S_3(z) -> T_2(z) we can infer forall z: W(z) -> T_2(z) via universal transitivity. Finally, from exists z: S(z) -> W(z), forall z: W(z) -> T_2(z) we can infer exists z: S(z) -> T_2(z) via existential transitivity. Therefore, the answer is yes.