Consider the following premises. forall x_4: P_4(x_4) and Q_4(x_4). Can we infer exists y_3: P_4(y_3) from them? If possible, name the inference rules being used at each step.
 From forall x_4: P_4(x_4) and Q_4(x_4) we can infer forall x_4: P_4(x_4) via universal simplification. From forall x_4: P_4(x_4) we can infer P_4(a) via universal instantiation. Finally, from P_4(a) we can infer exists y_3: P_4(y_3) via existential generalization. Therefore, the answer is yes.