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