Consider the following premises. p_9 -> r. r -> w. p_9 <-> w. Can we infer ~(r <-> p_9) from them?
 From p_9 <-> w we can infer w -> p_9. From r -> w, w -> p_9 we can infer r -> p_9. Finally, from r -> p_9, p_9 -> r we can infer r <-> p_9, which contradicts ~(r <-> p_9). Therefore, the answer is no.