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