Consider the following premises. If Karen were a doctor, then it is sunny. If it is sunny, then it is overcast. Karen is not a doctor. If it is overcast, then Karen is a doctor. 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 Karen were a doctor, then it is sunny, and that if it is sunny, then it is overcast we can infer that if Karen were a doctor, then it is overcast via transitivity. From the fact that if it is overcast, then Karen is a doctor, and that if Karen were a doctor, then it is overcast we can infer that it is overcast if and only if Karen is a doctor via biconditional introduction. Finally, from the fact that it is overcast if and only if Karen is a doctor, and that Karen is not a doctor we can infer that it is not overcast via biconditional elimination. Therefore, the answer is yes.