Consider the following premises. forall y: P_2(y) or ~W_1(y). forall y: P_2(y) -> T_3(y). forall y: T_3(y) -> W_1(y). Can we infer forall y: P_2(y) -> W_1(y) from them? If possible, name the inference rules being used at each step.
We can infer forall y: P_2(y) -> W_1(y) via the universal transitivity rule. Therefore, the answer is yes.