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