Consider the following premises. There is at least one y for which y is not an office clerk. For all y, if y were a bartender, then y is an office clerk. For all y, if y were an office clerk, then y is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is not a bartender.
 From the fact that for all y, if y were a bartender, then y is an office clerk, and that for all y, if y were an office clerk, then y is a bartender we can infer that for all y, y is a bartender if and only if y is an office clerk via universal biconditional introduction. Finally, from the fact that for all y, y is a bartender if and only if y is an office clerk, and that there is at least one y for which y is not an office clerk we can infer that there is at least one y for which y is not a bartender via existential biconditional elimination. Therefore, the answer is yes.