Consider the following premises. It is overcast or it is not sunny. It is sunny and Thomas is cooking. 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 sunny and Thomas is cooking we can infer that it is sunny via simplification. From the fact that it is overcast or it is not sunny we can infer that if it is sunny, then it is overcast via rewriting. Finally, from the fact that if it is sunny, then it is overcast, and that it is sunny we can infer that it is overcast via modus ponens. Therefore, the answer is yes.