Consider the following premises. forall x_9: Q_9(x_9) <-> P_9(x_9). forall x_9: P_9(x_9) or ~Q_9(x_9). Can we infer Q_9(a_2) -> P_9(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or ~Q_9(x_9) we can infer forall x_9: Q_9(x_9) -> P_9(x_9) via universal rewriting. From forall x_9: Q_9(x_9) <-> P_9(x_9) we can infer forall x_9: P_9(x_9) -> Q_9(x_9) via universal biconditional elimination. From forall x_9: P_9(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> P_9(x_9) we can infer forall x_9: P_9(x_9) <-> Q_9(x_9) via universal biconditional introduction. From forall x_9: P_9(x_9) <-> Q_9(x_9) we can infer P_9(a_2) <-> Q_9(a_2) via universal instantiation. Finally, from P_9(a_2) <-> Q_9(a_2) we can infer Q_9(a_2) -> P_9(a_2) via biconditional elimination. Therefore, the answer is yes.