Consider the following premises. For all y_1, if y_1 sleeps, then y_1 is a nurse. For all y_1, if y_1 were a bartender, then y_1 is sleeping. There is at least one y_1 for which y_1 will take a plane if and only if y_1 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which if y_1 were a bartender, then y_1 is taking a plane.
 From the fact that there is at least one y_1 for which y_1 will take a plane if and only if y_1 is a nurse we can infer that there is at least one y_1 for which if y_1 were a nurse, then y_1 is taking a plane via existential biconditional elimination. From the fact that for all y_1, if y_1 were a bartender, then y_1 is sleeping, and that for all y_1, if y_1 sleeps, then y_1 is a nurse we can infer that for all y_1, if y_1 were a bartender, then y_1 is a nurse via universal transitivity. Finally, from the fact that for all y_1, if y_1 were a bartender, then y_1 is a nurse, and that there is at least one y_1 for which if y_1 were a nurse, then y_1 is taking a plane we can infer that there is at least one y_1 for which if y_1 were a bartender, then y_1 is taking a plane via existential transitivity. Therefore, the answer is yes.