Consider the following premises. exists z_3: R_4(z_3) <-> Q(z_3). forall z_3: Q_3(z_3) <-> R_4(z_3). Can we infer exists z_3: Q(z_3) -> Q_3(z_3) from them? If possible, name the inference rules being used at each step.
 From exists z_3: R_4(z_3) <-> Q(z_3) we can infer exists z_3: Q(z_3) -> R_4(z_3) via existential biconditional elimination. From forall z_3: Q_3(z_3) <-> R_4(z_3) we can infer forall z_3: R_4(z_3) -> Q_3(z_3) via universal biconditional elimination. Finally, from exists z_3: Q(z_3) -> R_4(z_3), forall z_3: R_4(z_3) -> Q_3(z_3) we can infer exists z_3: Q(z_3) -> Q_3(z_3) via existential transitivity. Therefore, the answer is yes.