Consider the following premises. forall y: S(y) -> W_2(y). forall y: P(y) -> S(y). forall y: P(y) <-> P_1(y). Can we infer forall y: P_1(y) -> W_2(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P(y) <-> P_1(y) we can infer forall y: P_1(y) -> P(y) via universal biconditional elimination. From forall y: P_1(y) -> P(y), forall y: P(y) -> S(y) we can infer forall y: P_1(y) -> S(y) via universal transitivity. Finally, from forall y: P_1(y) -> S(y), forall y: S(y) -> W_2(y) we can infer forall y: P_1(y) -> W_2(y) via universal transitivity. Therefore, the answer is yes.