Consider the following premises. Susan is not writing a letter. Karen is a doctor if and only if Susan is writing a letter. If Karen were a doctor, then Susan is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Karen is not a doctor.
 From the fact that Karen is a doctor if and only if Susan is writing a letter we can infer that if Susan writes a letter, then Karen is a doctor via biconditional elimination. From the fact that if Susan writes a letter, then Karen is a doctor, and that if Karen were a doctor, then Susan is writing a letter we can infer that Susan is writing a letter if and only if Karen is a doctor via biconditional introduction. Finally, from the fact that Susan is writing a letter if and only if Karen is a doctor, and that Susan is not writing a letter we can infer that Karen is not a doctor via biconditional elimination. Therefore, the answer is yes.