Consider the following premises. forall z_2: R_4(z_2) or ~Q(z_2). exists z_2: R_4(z_2) -> Q(z_2). Can we infer exists z_2: Q(z_2) -> R_4(z_2) from them? If possible, name the inference rules being used at each step.
 From forall z_2: R_4(z_2) or ~Q(z_2) we can infer forall z_2: Q(z_2) -> R_4(z_2) via universal rewriting. From forall z_2: Q(z_2) -> R_4(z_2), exists z_2: R_4(z_2) -> Q(z_2) we can infer exists z_2: Q(z_2) <-> R_4(z_2) via existential biconditional introduction. Finally, from exists z_2: Q(z_2) <-> R_4(z_2) we can infer exists z_2: Q(z_2) -> R_4(z_2) via existential biconditional elimination. Therefore, the answer is yes.