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