Consider the following premises. For all x, x is a bartender and x will drive a car. There is at least one x for which if x were a bartender, then x is working. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will work.
 From the fact that for all x, x is a bartender and x will drive a car we can infer that for all x, x is a bartender via universal simplification. Finally, from the fact that there is at least one x for which if x were a bartender, then x is working, and that for all x, x is a bartender we can infer that there is at least one x for which x will work via existential modus ponens. Therefore, the answer is yes.