Consider the following premises. For all y, if y were an astronaut, then y is a cashier. For all y, y is an astronaut or y is not a scientist. For all y, if y were a cashier, then y is an astronaut. There is at least one y for which y is a scientist. Can we infer the following from them? There is at least one y for which y is a cashier.
 From the fact that for all y, y is an astronaut or y is not a scientist we can infer that for all y, if y were a scientist, then y is an astronaut. From the fact that for all y, if y were a cashier, then y is an astronaut, and that for all y, if y were an astronaut, then y is a cashier we can infer that for all y, y is a cashier if and only if y is an astronaut. From the fact that for all y, y is a cashier if and only if y is an astronaut we can infer that for all y, if y were an astronaut, then y is a cashier. From the fact that for all y, if y were a scientist, then y is an astronaut, and that there is at least one y for which y is a scientist we can infer that there is at least one y for which y is an astronaut. Finally, from the fact that for all y, if y were an astronaut, then y is a cashier, and that there is at least one y for which y is an astronaut we can infer that there is at least one y for which y is a cashier. Therefore, the answer is yes.