Consider the following premises. q -> q_6. q_6 -> q. q_6 -> q. Can we infer ~(q_6 <-> q) from them? If possible, name the inference rules being used at each step.
 From q -> q_6, q_6 -> q we can infer q <-> q_6 via biconditional introduction. From q <-> q_6 we can infer q -> q_6 via biconditional elimination. Finally, from q_6 -> q, q -> q_6 we can infer q_6 <-> q via biconditional introduction, which contradicts ~(q_6 <-> q). Therefore, the answer is no.