Consider the following premises. forall x_3: P_4(x_3) -> Q_3(x_3). forall x_3: Q_3(x_3) -> P_4(x_3). Can we infer Q_3(a_2) -> P_4(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_3: P_4(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> P_4(x_3) we can infer forall x_3: P_4(x_3) <-> Q_3(x_3) via universal biconditional introduction. From forall x_3: P_4(x_3) <-> Q_3(x_3) we can infer P_4(a_2) <-> Q_3(a_2) via universal instantiation. Finally, from P_4(a_2) <-> Q_3(a_2) we can infer Q_3(a_2) -> P_4(a_2) via biconditional elimination. Therefore, the answer is yes.