Consider the following premises. u -> r_3. ~u. r_3 <-> u. Can we infer ~r_3 from them? If possible, name the inference rules being used at each step.
 From r_3 <-> u we can infer r_3 -> u via biconditional elimination. From u -> r_3, r_3 -> u we can infer u <-> r_3 via biconditional introduction. Finally, from u <-> r_3, ~u we can infer ~r_3 via biconditional elimination. Therefore, the answer is yes.