Consider the following premises. u_4 <-> q_1. u -> q. q -> q_1. u_4 -> u. Can we infer u <-> q_1 from them? If possible, name the inference rules being used at each step.
 From u -> q, q -> q_1 we can infer u -> q_1 via transitivity. From u_4 <-> q_1 we can infer q_1 -> u_4 via biconditional elimination. From q_1 -> u_4, u_4 -> u we can infer q_1 -> u via transitivity. Finally, from u -> q_1, q_1 -> u we can infer u <-> q_1 via biconditional introduction. Therefore, the answer is yes.