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