Consider the following premises. p_9 <-> r. r or ~p_9. Can we infer ~(r <-> p_9) from them? If possible, name the inference rules being used at each step.
 From p_9 <-> r we can infer r -> p_9 via biconditional elimination. From r or ~p_9 we can infer p_9 -> r via rewriting. Finally, from r -> p_9, p_9 -> r we can infer r <-> p_9 via biconditional introduction, which contradicts ~(r <-> p_9). Therefore, the answer is no.