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