Consider the following premises. p. w -> p_5. p_5 <-> w. w -> ~p. Can we infer p_5 from them?
 From w -> ~p, p we can infer ~w. From p_5 <-> w we can infer p_5 -> w. From p_5 -> w, w -> p_5 we can infer p_5 <-> w. Finally, from p_5 <-> w, ~w we can infer ~p_5, which contradicts p_5. Therefore, the answer is no.