Consider the following premises. forall z: W_4(z) <-> P_2(z). exists z: P_2(z) <-> W_4(z). Can we infer exists z: W_4(z) <-> P_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W_4(z) <-> P_2(z) we can infer forall z: W_4(z) -> P_2(z) via universal biconditional elimination. From exists z: P_2(z) <-> W_4(z) we can infer exists z: P_2(z) -> W_4(z) via existential biconditional elimination. Finally, from forall z: W_4(z) -> P_2(z), exists z: P_2(z) -> W_4(z) we can infer exists z: W_4(z) <-> P_2(z) via existential biconditional introduction. Therefore, the answer is yes.