Consider the following premises. exists z: U_1(z) -> W(z). forall z: W(z) <-> U_1(z). Can we infer exists z: U_1(z) <-> W(z) from them?
 From forall z: W(z) <-> U_1(z) we can infer forall z: W(z) -> U_1(z). Finally, from exists z: U_1(z) -> W(z), forall z: W(z) -> U_1(z) we can infer exists z: U_1(z) <-> W(z). Therefore, the answer is yes.