Consider the following premises. For all x_9, if x_9 were a nurse, then x_9 is a bartender. There is at least one x_9 for which x_9 is rich or x_9 is sad. For all x_9, if x_9 were rich, then x_9 is a nurse. For all x_9, if x_9 were sad, then x_9 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is a bartender.
 From the fact that for all x_9, if x_9 were rich, then x_9 is a nurse, that for all x_9, if x_9 were sad, then x_9 is a nurse, and that there is at least one x_9 for which x_9 is rich or x_9 is sad we can infer that there is at least one x_9 for which x_9 is a nurse via existential disjunction elimination. Finally, from the fact that for all x_9, if x_9 were a nurse, then x_9 is a bartender, and that there is at least one x_9 for which x_9 is a nurse we can infer that there is at least one x_9 for which x_9 is a bartender via existential modus ponens. Therefore, the answer is yes.