Consider the following premises. forall z: W(z) <-> R_4(z). exists z: W(z) -> R_4(z). forall z: R_4(z) or ~Q(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: W(z) <-> R_4(z) we can infer forall z: R_4(z) -> W(z) via universal biconditional elimination. From forall z: R_4(z) -> W(z), exists z: W(z) -> R_4(z) we can infer exists z: R_4(z) <-> W(z) via existential biconditional introduction. From exists z: R_4(z) <-> W(z) we can infer exists z: R_4(z) -> W(z) via existential biconditional elimination. From forall z: R_4(z) or ~Q(z) we can infer forall z: Q(z) -> R_4(z) via universal rewriting. Finally, from forall z: Q(z) -> R_4(z), exists z: R_4(z) -> W(z) we can infer exists z: Q(z) -> W(z) via existential transitivity. Therefore, the answer is yes.