Consider the following premises. p_1 -> p_8. p_8 -> p. p <-> p_1. p_1 -> p_8. Can we infer p_8 <-> p_1 from them?
 From p <-> p_1 we can infer p -> p_1. From p_8 -> p, p -> p_1 we can infer p_8 -> p_1. Finally, from p_8 -> p_1, p_1 -> p_8 we can infer p_8 <-> p_1. Therefore, the answer is yes.