Consider the following premises. Thomas is sleeping if and only if Richard is working. If Richard works, then Thomas is taking a plane. It is not sunny. Thomas is taking a plane if and only if it is sunny. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not sleeping.
 From the fact that Thomas is taking a plane if and only if it is sunny, and that it is not sunny we can infer that Thomas is not taking a plane via biconditional elimination. From the fact that if Richard works, then Thomas is taking a plane, and that Thomas is not taking a plane we can infer that Richard is not working via modus tollens. Finally, from the fact that Thomas is sleeping if and only if Richard is working, and that Richard is not working we can infer that Thomas is not sleeping via biconditional elimination. Therefore, the answer is yes.