Consider the following premises. w_4 <-> r. w <-> r. Can we infer ~(w_4 -> w) from them?
 From w_4 <-> r we can infer w_4 -> r. From w <-> r we can infer r -> w. Finally, from w_4 -> r, r -> w we can infer w_4 -> w, which contradicts ~(w_4 -> w). Therefore, the answer is no.