Consider the following premises. forall x_7: P_7(x_7) and Q_7(x_7). forall x_7: P_3(x_7) and Q_3(x_7). Can we infer forall x_7: P_3(x_7) and P_7(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) and Q_7(x_7) we can infer forall x_7: P_7(x_7) via universal simplification. From forall x_7: P_3(x_7) and Q_3(x_7) we can infer forall x_7: P_3(x_7) via universal simplification. Finally, from forall x_7: P_3(x_7), forall x_7: P_7(x_7) we can infer forall x_7: P_3(x_7) and P_7(x_7) via universal conjunction. Therefore, the answer is yes.