Consider the following premises. It is cold and Charles is playing tennis. It is windy. If it rains, then Mary is sleeping. If it is windy, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if it is windy, then it is raining, and that it is windy we can infer that it is raining via modus ponens. From the fact that if it rains, then Mary is sleeping, and that it is raining we can infer that Mary is sleeping via modus ponens. Finally, from the fact that it is cold and Charles is playing tennis we can infer that it is cold via simplification, which contradicts that It is not cold. Therefore, the answer is no.