Consider the following premises. exists z: Q_4(z) <-> S(z). forall z: Q_4(z) -> S(z). Can we infer exists z: Q_4(z) -> S(z) from them? If possible, name the inference rules being used at each step.
 From exists z: Q_4(z) <-> S(z) we can infer exists z: S(z) -> Q_4(z) via existential biconditional elimination. From exists z: S(z) -> Q_4(z), forall z: Q_4(z) -> S(z) we can infer exists z: S(z) <-> Q_4(z) via existential biconditional introduction. Finally, from exists z: S(z) <-> Q_4(z) we can infer exists z: Q_4(z) -> S(z) via existential biconditional elimination. Therefore, the answer is yes.