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