Consider the following premises. r_2 <-> u. u or ~r_2. u -> r_2. Can we infer ~(u <-> r_2) from them? If possible, name the inference rules being used at each step.
 From u or ~r_2 we can infer r_2 -> u via rewriting. From r_2 <-> u we can infer r_2 -> u via biconditional elimination. Finally, from u -> r_2, r_2 -> u we can infer u <-> r_2 via biconditional introduction, which contradicts ~(u <-> r_2). Therefore, the answer is no.