Consider the following premises. For all x_5, if x_5 were a doctor, then x_5 is writing a letter. For all x_3, x_3 is a police officer. For all x_3, if x_3 were a police officer, then x_3 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: David is writing a letter.
 From the fact that for all x_3, if x_3 were a police officer, then x_3 is a doctor, and that for all x_3, x_3 is a police officer we can infer that for all x_3, x_3 is a doctor via universal modus ponens. From the fact that for all x_3, x_3 is a doctor we can infer that David is a doctor via universal instantiation. From the fact that for all x_5, if x_5 were a doctor, then x_5 is writing a letter we can infer that if David were a doctor, then David is writing a letter via universal instantiation. Finally, from the fact that if David were a doctor, then David is writing a letter, and that David is a doctor we can infer that David is writing a letter via modus ponens. Therefore, the answer is yes.