Consider the following premises. q or ~q_9. q -> q_9. q_9 -> ~q_4. q_4. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From q or ~q_9 we can infer q_9 -> q via rewriting. From q_9 -> ~q_4, q_4 we can infer ~q_9 via modus tollens. From q -> q_9, q_9 -> q we can infer q <-> q_9 via biconditional introduction. Finally, from q <-> q_9, ~q_9 we can infer ~q via biconditional elimination. Therefore, the answer is yes.