Consider the following premises. u <-> w. p_4 -> u. u -> p_4. Can we infer p_4 -> w from them?
 From p_4 -> u, u -> p_4 we can infer p_4 <-> u. From u <-> w we can infer u -> w. From p_4 <-> u we can infer p_4 -> u. Finally, from p_4 -> u, u -> w we can infer p_4 -> w. Therefore, the answer is yes.