Consider the following premises. R_7(a_7) <-> p. forall x_7: R_7(x_7) <-> S_7(x_7). ~p. Can we infer ~S_7(a_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(a_7) <-> S_7(a_7) via universal instantiation. From R_7(a_7) <-> p, ~p we can infer ~R_7(a_7) via biconditional elimination. Finally, from R_7(a_7) <-> S_7(a_7), ~R_7(a_7) we can infer ~S_7(a_7) via biconditional elimination. Therefore, the answer is yes.