Consider the following premises. p_3 -> r. u -> p_3. ~r. r <-> u. Can we infer ~p_3 from them?
 From r <-> u we can infer r -> u. From r -> u, u -> p_3 we can infer r -> p_3. From p_3 -> r, r -> p_3 we can infer p_3 <-> r. Finally, from p_3 <-> r, ~r we can infer ~p_3. Therefore, the answer is yes.