Consider the following premises. There is at least one x_15 for which x_15 is poor. For all x_15, x_15 will work if and only if x_15 is poor. For all x_15, x_15 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 is a bartender.
 From the fact that for all x_15, x_15 will work if and only if x_15 is poor we can infer that for all x_15, if x_15 were poor, then x_15 is working via universal biconditional elimination. From the fact that for all x_15, if x_15 were poor, then x_15 is working, and that there is at least one x_15 for which x_15 is poor we can infer that there is at least one x_15 for which x_15 will work via existential modus ponens. From the fact that for all x_15, x_15 is a bartender, and that there is at least one x_15 for which x_15 will work we can infer that some bartenders will work via existential conjunction. Finally, from the fact that some bartenders will work we can infer that there is at least one x_15 for which x_15 is a bartender via existential simplification. Therefore, the answer is yes.