Consider the following premises. forall z: W_2(z) -> R(z). forall z: T(z) or R(z). exists z: T(z) -> W_2(z). forall z: R(z) -> W_2(z). Can we infer exists z: W_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: R(z) -> W_2(z), forall z: W_2(z) -> R(z) we can infer forall z: R(z) <-> W_2(z) via universal biconditional introduction. From forall z: R(z) <-> W_2(z) we can infer forall z: R(z) -> W_2(z) via universal biconditional elimination. Finally, from exists z: T(z) -> W_2(z), forall z: R(z) -> W_2(z), forall z: T(z) or R(z) we can infer exists z: W_2(z) via existential disjunction elimination. Therefore, the answer is yes.