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