Consider the following premises. forall z: U_4(z) <-> S_1(z). forall z: U_4(z) <-> S_1(z). Can we infer forall z: S_1(z) <-> U_4(z) from them?
 From forall z: U_4(z) <-> S_1(z) we can infer forall z: U_4(z) -> S_1(z). From forall z: U_4(z) <-> S_1(z) we can infer forall z: S_1(z) -> U_4(z). Finally, from forall z: S_1(z) -> U_4(z), forall z: U_4(z) -> S_1(z) we can infer forall z: S_1(z) <-> U_4(z). Therefore, the answer is yes.