Consider the following premises. If Barbara writes a letter, then William is driving a car. David is excited if and only if Barbara is writing a letter. David is excited or William is not driving a car. Can we infer the following from them? If David were excited, then Barbara is writing a letter.
 From the fact that David is excited or William is not driving a car we can infer that if William drives a car, then David is excited. From the fact that if Barbara writes a letter, then William is driving a car, and that if William drives a car, then David is excited we can infer that if Barbara writes a letter, then David is excited. Finally, from the fact that David is excited if and only if Barbara is writing a letter we can infer that if David were excited, then Barbara is writing a letter. Therefore, the answer is yes.