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