Consider the following premises. forall x_10: P_10(x_10) -> W(x_10). forall x_10: P_10(x_10). w. Can we infer w and W(a_9) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> W(x_10), forall x_10: P_10(x_10) we can infer forall x_10: W(x_10) via universal modus ponens. From forall x_10: W(x_10) we can infer W(a_9) via universal instantiation. Finally, from w, W(a_9) we can infer w and W(a_9) via conjunction. Therefore, the answer is yes.