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