Consider the following premises. r -> r_1. r_2 <-> r. r_1 -> r_2. Can we infer r <-> r_2 from them?
 From r_2 <-> r we can infer r_2 -> r. From r -> r_1, r_1 -> r_2 we can infer r -> r_2. Finally, from r -> r_2, r_2 -> r we can infer r <-> r_2. Therefore, the answer is yes.