Consider the following premises. If it is overcast, then Thomas is writing a letter. Richard is poor if and only if it is overcast. Richard is poor. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not writing a letter.
 From the fact that Richard is poor if and only if it is overcast we can infer that if Richard were poor, then it is overcast via biconditional elimination. From the fact that if Richard were poor, then it is overcast, and that Richard is poor we can infer that it is overcast via modus ponens. Finally, from the fact that if it is overcast, then Thomas is writing a letter, and that it is overcast we can infer that Thomas is writing a letter via modus ponens, which contradicts that Thomas is not writing a letter. Therefore, the answer is no.