Consider the following premises. q -> p_13. p_13 -> q. q -> p_13. q -> ~q_9. q_9. Can we infer ~p_13 from them? If possible, name the inference rules being used at each step.
 From p_13 -> q, q -> p_13 we can infer p_13 <-> q via biconditional introduction. From q -> ~q_9, q_9 we can infer ~q via modus tollens. From p_13 <-> q we can infer p_13 -> q via biconditional elimination. From q -> p_13, p_13 -> q we can infer q <-> p_13 via biconditional introduction. Finally, from q <-> p_13, ~q we can infer ~p_13 via biconditional elimination. Therefore, the answer is yes.