Consider the following premises. forall x_4: W(x_4) <-> S_1(x_4). forall x_4: S_1(x_4) -> Q(x_4). forall x_4: Q(x_4) -> P_3(x_4). Can we infer forall x_4: W(x_4) -> P_3(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: W(x_4) <-> S_1(x_4) we can infer forall x_4: W(x_4) -> S_1(x_4) via universal biconditional elimination. From forall x_4: W(x_4) -> S_1(x_4), forall x_4: S_1(x_4) -> Q(x_4) we can infer forall x_4: W(x_4) -> Q(x_4) via universal transitivity. Finally, from forall x_4: W(x_4) -> Q(x_4), forall x_4: Q(x_4) -> P_3(x_4) we can infer forall x_4: W(x_4) -> P_3(x_4) via universal transitivity. Therefore, the answer is yes.