Consider the following premises. If Robert listens to a song, then Patricia is excited. If Patricia were a doctor, then Thomas is a bartender. For all x_10, if x_10 were excited, then x_10 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: If Robert listens to a song, then Thomas is a bartender.
 From the fact that for all x_10, if x_10 were excited, then x_10 is a doctor we can infer that if Patricia were excited, then Patricia is a doctor via universal instantiation. From the fact that if Robert listens to a song, then Patricia is excited, and that if Patricia were excited, then Patricia is a doctor we can infer that if Robert listens to a song, then Patricia is a doctor via transitivity. Finally, from the fact that if Robert listens to a song, then Patricia is a doctor, and that if Patricia were a doctor, then Thomas is a bartender we can infer that if Robert listens to a song, then Thomas is a bartender via transitivity. Therefore, the answer is yes.