Consider the following premises. forall x_2: W_3(x_2) <-> P_1(x_2). forall x_2: S(x_2) -> P_1(x_2). forall x_2: W_3(x_2) -> S(x_2). Can we infer forall x_2: W_3(x_2) -> P_1(x_2) from them? If possible, name the inference rules being used at each step.
We can infer forall x_2: W_3(x_2) -> P_1(x_2) via the universal transitivity rule. Therefore, the answer is yes.