Consider the following premises. p_12 <-> u. ~p_12. p_4 <-> ~u. Can we infer p_4 from them? If possible, name the inference rules being used at each step.
 From p_12 <-> u, ~p_12 we can infer ~u via biconditional elimination. From p_4 <-> ~u we can infer ~u -> p_4 via biconditional elimination. Finally, from ~u -> p_4, ~u we can infer p_4 via modus ponens. Therefore, the answer is yes.