Consider the following premises. For all z, z is a cashier if and only if z is an astronaut. For all z, if z were an astronaut, then z is a cashier. There is at least one z for which z is not an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all z, if z were an astronaut, then z is a cashier.
That is one of the premises. Therefore, the answer is yes.