Consider the following premises. u -> p_6. ~p_6. w <-> u. p_6 -> u. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From p_6 -> u, u -> p_6 we can infer p_6 <-> u via biconditional introduction. From p_6 <-> u, ~p_6 we can infer ~u via biconditional elimination. Finally, from w <-> u, ~u we can infer ~w via biconditional elimination. Therefore, the answer is yes.