Consider the following premises. If Thomas were an artist, then David is playing a game. For all x_23, x_23 will not write a letter. If David plays a game, then Thomas is an artist. If Barbara were a doctor, then John is writing a letter. David is not playing a game. Can we infer the following from them? If we can, name the inference rule being used: If Barbara were not a doctor, then Thomas is not an artist.
We cannot infer that from the premises. Therefore the answer is no.