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