Consider the following premises. ~u. u -> u_3. u <-> u_3. Can we infer u_3 from them? If possible, name the inference rules being used at each step.
 From u <-> u_3 we can infer u_3 -> u via biconditional elimination. From u -> u_3, u_3 -> u we can infer u <-> u_3 via biconditional introduction. Finally, from u <-> u_3, ~u we can infer ~u_3 via biconditional elimination, which contradicts u_3. Therefore, the answer is no.