Consider the following premises. If Thomas were a sailor, then Jessica is sleeping. John is happy. If Jessica sleeps, then Thomas is a sailor. If Jessica sleeps, then John is not happy. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not a sailor.
 From the fact that if Thomas were a sailor, then Jessica is sleeping, and that if Jessica sleeps, then Thomas is a sailor we can infer that Thomas is a sailor if and only if Jessica is sleeping via biconditional introduction. From the fact that if Jessica sleeps, then John is not happy, and that John is happy we can infer that Jessica is not sleeping via modus tollens. Finally, from the fact that Thomas is a sailor if and only if Jessica is sleeping, and that Jessica is not sleeping we can infer that Thomas is not a sailor via biconditional elimination. Therefore, the answer is yes.