Consider the following premises. forall z: T_4(z) -> P(z). exists z: T_4(z) <-> P(z). Can we infer exists z: T_4(z) -> P(z) from them? If possible, name the inference rules being used at each step.
 From exists z: T_4(z) <-> P(z) we can infer exists z: P(z) -> T_4(z) via existential biconditional elimination. From exists z: P(z) -> T_4(z), forall z: T_4(z) -> P(z) we can infer exists z: P(z) <-> T_4(z) via existential biconditional introduction. Finally, from exists z: P(z) <-> T_4(z) we can infer exists z: T_4(z) -> P(z) via existential biconditional elimination. Therefore, the answer is yes.