Consider the following premises. q or ~r_4. r_4 <-> q. Can we infer ~(r_4 -> q) from them? If possible, name the inference rules being used at each step.
 From r_4 <-> q we can infer q -> r_4 via biconditional elimination. Finally, from q or ~r_4 we can infer r_4 -> q via rewriting, which contradicts ~(r_4 -> q). Therefore, the answer is no.