Consider the following premises. forall x_4: P_3(x_4). forall x_4: P_4(x_4). forall x_4: P_4(x_4) -> Q_4(x_4). Can we infer Q_4(j_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: P_4(x_4) -> Q_4(x_4), forall x_4: P_4(x_4) we can infer forall x_4: Q_4(x_4) via universal modus ponens. From forall x_4: P_3(x_4), forall x_4: Q_4(x_4) we can infer forall x_4: P_3(x_4) and Q_4(x_4) via universal conjunction. From forall x_4: P_3(x_4) and Q_4(x_4) we can infer P_3(j_4) and Q_4(j_4) via universal instantiation. Finally, from P_3(j_4) and Q_4(j_4) we can infer Q_4(j_4) via simplification. Therefore, the answer is yes.