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