Consider the following premises. If it rains, then it is sunny. It is not raining. It is raining or it is not sunny. Can we infer the following from them? It is not sunny.
 From the fact that it is raining or it is not sunny we can infer that if it is sunny, then it is raining. From the fact that if it rains, then it is sunny, and that if it is sunny, then it is raining we can infer that it is raining if and only if it is sunny. Finally, from the fact that it is raining if and only if it is sunny, and that it is not raining we can infer that it is not sunny. Therefore, the answer is yes.