Consider the following premises. There is at least one y for which y is a cashier if and only if y will listen to a song. For all y, y will listen to a song. 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 a cashier.
 From the fact that there is at least one y for which y is a cashier if and only if y will listen to a song we can infer that there is at least one y for which if y listens to a song, then y is a cashier via existential biconditional elimination. Finally, from the fact that there is at least one y for which if y listens to a song, then y is a cashier, and that for all y, y will listen to a song we can infer that there is at least one y for which y is a cashier via existential modus ponens. Therefore, the answer is yes.