Consider the following premises. u -> p_4. u_4 -> u. p_4 -> u_4. ~u_4. Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From u_4 -> u, u -> p_4 we can infer u_4 -> p_4 via transitivity. From p_4 -> u_4, u_4 -> p_4 we can infer p_4 <-> u_4 via biconditional introduction. Finally, from p_4 <-> u_4, ~u_4 we can infer ~p_4 via biconditional elimination. Therefore, the answer is yes.