Consider the following premises. forall z: P(z) -> R_1(z). exists z: P(z) <-> R_1(z). Can we infer exists z: P(z) -> R_1(z) from them? If possible, name the inference rules being used at each step.
 From exists z: P(z) <-> R_1(z) we can infer exists z: R_1(z) -> P(z) via existential biconditional elimination. From forall z: P(z) -> R_1(z), exists z: R_1(z) -> P(z) we can infer exists z: P(z) <-> R_1(z) via existential biconditional introduction. Finally, from exists z: P(z) <-> R_1(z) we can infer exists z: P(z) -> R_1(z) via existential biconditional elimination. Therefore, the answer is yes.