Consider the following premises. p_4 <-> q. ~p. p <-> p_4. Can we infer q from them? If possible, name the inference rules being used at each step.
 From p <-> p_4, ~p we can infer ~p_4 via biconditional elimination. Finally, from p_4 <-> q, ~p_4 we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.