Consider the following premises. p_1 -> r_3. p -> p_1. r_3 -> u. u -> p. Can we infer p <-> p_1 from them?
 From r_3 -> u, u -> p we can infer r_3 -> p. From p_1 -> r_3, r_3 -> p we can infer p_1 -> p. Finally, from p -> p_1, p_1 -> p we can infer p <-> p_1. Therefore, the answer is yes.