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