Consider the following premises. q <-> r_6. u -> r_6. q <-> u. Can we infer ~(r_6 <-> q) from them? If possible, name the inference rules being used at each step.
 From q <-> u we can infer q -> u via biconditional elimination. From q -> u, u -> r_6 we can infer q -> r_6 via transitivity. From q <-> r_6 we can infer r_6 -> q via biconditional elimination. Finally, from r_6 -> q, q -> r_6 we can infer r_6 <-> q via biconditional introduction, which contradicts ~(r_6 <-> q). Therefore, the answer is no.