Consider the following premises. exists z_2: U_2(z_2) <-> W_2(z_2). forall z_2: R_4(z_2) -> W(z_2). forall z_2: W(z_2) -> W_2(z_2). Can we infer exists z_2: R_4(z_2) -> U_2(z_2) from them? If possible, name the inference rules being used at each step.
 From exists z_2: U_2(z_2) <-> W_2(z_2) we can infer exists z_2: W_2(z_2) -> U_2(z_2) via existential biconditional elimination. From forall z_2: R_4(z_2) -> W(z_2), forall z_2: W(z_2) -> W_2(z_2) we can infer forall z_2: R_4(z_2) -> W_2(z_2) via universal transitivity. Finally, from forall z_2: R_4(z_2) -> W_2(z_2), exists z_2: W_2(z_2) -> U_2(z_2) we can infer exists z_2: R_4(z_2) -> U_2(z_2) via existential transitivity. Therefore, the answer is yes.