Consider the following premises. forall x_7: Q_7(x_7). forall x_7: R(x_7) -> ~Q_7(x_7). r <-> R(a_5). Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From forall x_7: R(x_7) -> ~Q_7(x_7), forall x_7: Q_7(x_7) we can infer forall x_7: ~R(x_7) via universal modus tollens. From forall x_7: ~R(x_7) we can infer ~R(a_5) via universal instantiation. Finally, from r <-> R(a_5), ~R(a_5) we can infer ~r via biconditional elimination. Therefore, the answer is yes.