Consider the following premises. u_2 -> p_13. p_13 -> u_2. p_13 <-> u_1. p_13 -> u_2. ~u_1. Can we infer ~u_2 from them? If possible, name the inference rules being used at each step.
 From p_13 -> u_2, u_2 -> p_13 we can infer p_13 <-> u_2 via biconditional introduction. From p_13 <-> u_2 we can infer u_2 -> p_13 via biconditional elimination. From p_13 <-> u_1, ~u_1 we can infer ~p_13 via biconditional elimination. From u_2 -> p_13, p_13 -> u_2 we can infer u_2 <-> p_13 via biconditional introduction. Finally, from u_2 <-> p_13, ~p_13 we can infer ~u_2 via biconditional elimination. Therefore, the answer is yes.