Consider the following premises. t_2 -> u. t_2 -> u. u -> t_2. Can we infer ~(u <-> t_2) from them? If possible, name the inference rules being used at each step.
 From t_2 -> u, u -> t_2 we can infer t_2 <-> u via biconditional introduction. From t_2 <-> u we can infer u -> t_2 via biconditional elimination. Finally, from u -> t_2, t_2 -> u we can infer u <-> t_2 via biconditional introduction, which contradicts ~(u <-> t_2). Therefore, the answer is no.