Consider the following premises. If it is windy, then it is raining. It is windy and William is sleeping. If it rains, then it is late. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that if it is windy, then it is raining, and that if it rains, then it is late we can infer that if it is windy, then it is late via transitivity. From the fact that it is windy and William is sleeping we can infer that it is windy via simplification. Finally, from the fact that if it is windy, then it is late, and that it is windy we can infer that it is late via modus ponens. Therefore, the answer is yes.