Consider the following premises. p_13 <-> q_13. p_9 <-> q_13. p_9 -> p_13. Can we infer ~(q_13 <-> p_13) from them? If possible, name the inference rules being used at each step.
 From p_13 <-> q_13 we can infer p_13 -> q_13 via biconditional elimination. From p_9 <-> q_13 we can infer q_13 -> p_9 via biconditional elimination. From q_13 -> p_9, p_9 -> p_13 we can infer q_13 -> p_13 via transitivity. Finally, from q_13 -> p_13, p_13 -> q_13 we can infer q_13 <-> p_13 via biconditional introduction, which contradicts ~(q_13 <-> p_13). Therefore, the answer is no.