Consider the following premises. p_3 <-> q. p_1 -> q. p_3 -> p_1. Can we infer p_1 <-> p_3 from them?
 From p_3 <-> q we can infer q -> p_3. From p_1 -> q, q -> p_3 we can infer p_1 -> p_3. Finally, from p_1 -> p_3, p_3 -> p_1 we can infer p_1 <-> p_3. Therefore, the answer is yes.