Consider the following premises. s_3 -> u. u -> s_3. s_3 -> u. Can we infer ~(u <-> s_3) from them? If possible, name the inference rules being used at each step.
 From s_3 -> u, u -> s_3 we can infer s_3 <-> u via biconditional introduction. From s_3 <-> u we can infer u -> s_3 via biconditional elimination. Finally, from u -> s_3, s_3 -> u we can infer u <-> s_3 via biconditional introduction, which contradicts ~(u <-> s_3). Therefore, the answer is no.