Consider the following premises. Thomas is working if and only if Richard is cooking. If Charles were a doctor, then Richard is cooking. Thomas is not working. If Thomas works, then Richard is cooking. Can we infer the following from them? If we can, name the inference rule being used: Charles is not a doctor.
 From the fact that Thomas is working if and only if Richard is cooking we can infer that if Richard cooks, then Thomas is working via biconditional elimination. From the fact that if Richard cooks, then Thomas is working, and that if Thomas works, then Richard is cooking we can infer that Richard is cooking if and only if Thomas is working via biconditional introduction. From the fact that Richard is cooking if and only if Thomas is working, and that Thomas is not working we can infer that Richard is not cooking via biconditional elimination. Finally, from the fact that if Charles were a doctor, then Richard is cooking, and that Richard is not cooking we can infer that Charles is not a doctor via modus tollens. Therefore, the answer is yes.