Consider the following premises. q -> t_1. r_1 -> q. t_1 <-> r_1. Can we infer ~(r_1 <-> q) from them? If possible, name the inference rules being used at each step.
 From t_1 <-> r_1 we can infer t_1 -> r_1 via biconditional elimination. From q -> t_1, t_1 -> r_1 we can infer q -> r_1 via transitivity. Finally, from r_1 -> q, q -> r_1 we can infer r_1 <-> q via biconditional introduction, which contradicts ~(r_1 <-> q). Therefore, the answer is no.