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