Consider the following premises. u <-> r. r -> p_1. p_1 -> u. Can we infer r <-> p_1 from them? If possible, name the inference rules being used at each step.
 From u <-> r we can infer u -> r via biconditional elimination. From p_1 -> u, u -> r we can infer p_1 -> r via transitivity. Finally, from r -> p_1, p_1 -> r we can infer r <-> p_1 via biconditional introduction. Therefore, the answer is yes.