Consider the following premises. ~p_2. u_3 -> p_2. p_2 <-> u_3. Can we infer u_3 from them? If possible, name the inference rules being used at each step.
 From p_2 <-> u_3 we can infer p_2 -> u_3 via biconditional elimination. From u_3 -> p_2, p_2 -> u_3 we can infer u_3 <-> p_2 via biconditional introduction. Finally, from u_3 <-> p_2, ~p_2 we can infer ~u_3 via biconditional elimination, which contradicts u_3. Therefore, the answer is no.