Consider the following premises. w <-> w_2. r -> w_2. w_2 -> r. Can we infer r -> w from them?
 From w_2 -> r, r -> w_2 we can infer w_2 <-> r. From w <-> w_2 we can infer w_2 -> w. From w_2 <-> r we can infer r -> w_2. Finally, from r -> w_2, w_2 -> w we can infer r -> w. Therefore, the answer is yes.