Consider the following premises. r -> q_3. p_10 <-> q_10. q_3 -> q_10. q_10 -> r. ~p_10. Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From p_10 <-> q_10, ~p_10 we can infer ~q_10 via biconditional elimination. From r -> q_3, q_3 -> q_10 we can infer r -> q_10 via transitivity. From r -> q_10, q_10 -> r we can infer r <-> q_10 via biconditional introduction. Finally, from r <-> q_10, ~q_10 we can infer ~r via biconditional elimination. Therefore, the answer is yes.