Consider the following premises. If Charles were not a janitor, then William is a lawyer. If William were a lawyer, then William is a doctor. Linda is not a poet. Linda is a poet if and only if Charles is a janitor. Can we infer the following from them? If we can, name the inference rule being used: William is a doctor.
 From the fact that Linda is a poet if and only if Charles is a janitor, and that Linda is not a poet we can infer that Charles is not a janitor via biconditional elimination. From the fact that if Charles were not a janitor, then William is a lawyer, and that if William were a lawyer, then William is a doctor we can infer that if Charles were not a janitor, then William is a doctor via transitivity. Finally, from the fact that if Charles were not a janitor, then William is a doctor, and that Charles is not a janitor we can infer that William is a doctor via modus ponens. Therefore, the answer is yes.