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