Consider the following premises. John is not a janitor. For all y, if y were a janitor, then y is an astronaut. For all y, if y were an astronaut, then y is a janitor. Can we infer the following from them? If we can, name the inference rule being used: John is an astronaut.
 From the fact that for all y, if y were a janitor, then y is an astronaut, and that for all y, if y were an astronaut, then y is a janitor we can infer that for all y, y is a janitor if and only if y is an astronaut via universal biconditional introduction. From the fact that for all y, y is a janitor if and only if y is an astronaut we can infer that John is a janitor if and only if John is an astronaut via universal instantiation. Finally, from the fact that John is a janitor if and only if John is an astronaut, and that John is not a janitor we can infer that John is not an astronaut via biconditional elimination, which contradicts that John is an astronaut. Therefore, the answer is no.