Consider the following premises. forall y: Q_3(y) -> P_4(y). w_3 or ~P_4(a_10). Can we infer Q_3(a_10) -> w_3 from them? If possible, name the inference rules being used at each step.
 From forall y: Q_3(y) -> P_4(y) we can infer Q_3(a_10) -> P_4(a_10) via universal instantiation. From w_3 or ~P_4(a_10) we can infer P_4(a_10) -> w_3 via rewriting. Finally, from Q_3(a_10) -> P_4(a_10), P_4(a_10) -> w_3 we can infer Q_3(a_10) -> w_3 via transitivity. Therefore, the answer is yes.