Consider the following premises. p <-> P_9(a_5). forall x_9: ~Q_9(x_9). forall x_9: P_9(x_9) <-> Q_9(x_9). Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) <-> Q_9(x_9), forall x_9: ~Q_9(x_9) we can infer forall x_9: ~P_9(x_9) via universal biconditional elimination. From forall x_9: ~P_9(x_9) we can infer ~P_9(a_5) via universal instantiation. Finally, from p <-> P_9(a_5), ~P_9(a_5) we can infer ~p via biconditional elimination. Therefore, the answer is yes.