Consider the following premises. r -> p_10. ~p. p_10 <-> r. p <-> r. Can we infer p_10 from them? If possible, name the inference rules being used at each step.
 From p_10 <-> r we can infer p_10 -> r via biconditional elimination. From p_10 -> r, r -> p_10 we can infer p_10 <-> r via biconditional introduction. From p <-> r, ~p we can infer ~r via biconditional elimination. Finally, from p_10 <-> r, ~r we can infer ~p_10 via biconditional elimination, which contradicts p_10. Therefore, the answer is no.