Consider the following premises. If David were an artist, then Barbara is writing a letter. David is not an artist. If it snows, then David is an artist. If Barbara writes a letter, then it is snowing. Can we infer the following from them? Barbara is not writing a letter.
 From the fact that if Barbara writes a letter, then it is snowing, and that if it snows, then David is an artist we can infer that if Barbara writes a letter, then David is an artist. From the fact that if David were an artist, then Barbara is writing a letter, and that if Barbara writes a letter, then David is an artist we can infer that David is an artist if and only if Barbara is writing a letter. Finally, from the fact that David is an artist if and only if Barbara is writing a letter, and that David is not an artist we can infer that Barbara is not writing a letter. Therefore, the answer is yes.