Consider the following premises. exists z: W(z) -> U_4(z). forall z: S_4(z) or ~U_4(z). forall z: S_4(z) -> W(z). Can we infer exists z: S_4(z) <-> U_4(z) from them? If possible, name the inference rules being used at each step.
 From forall z: S_4(z) or ~U_4(z) we can infer forall z: U_4(z) -> S_4(z) via universal rewriting. From forall z: S_4(z) -> W(z), exists z: W(z) -> U_4(z) we can infer exists z: S_4(z) -> U_4(z) via existential transitivity. Finally, from exists z: S_4(z) -> U_4(z), forall z: U_4(z) -> S_4(z) we can infer exists z: S_4(z) <-> U_4(z) via existential biconditional introduction. Therefore, the answer is yes.