Consider the following premises. If it rains, then it is sunny. If it is sunny, then it is overcast. Thomas is not poor. If it is sunny, then Thomas is poor. If it is overcast, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that if it is overcast, then it is raining, and that if it rains, then it is sunny we can infer that if it is overcast, then it is sunny via transitivity. From the fact that if it is sunny, then it is overcast, and that if it is overcast, then it is sunny we can infer that it is sunny if and only if it is overcast via biconditional introduction. From the fact that if it is sunny, then Thomas is poor, and that Thomas is not poor we can infer that it is not sunny via modus tollens. Finally, from the fact that it is sunny if and only if it is overcast, and that it is not sunny we can infer that it is not overcast via biconditional elimination. Therefore, the answer is yes.