Consider the following premises. For all y, y is rich. There is at least one y for which y is an astronaut if and only if y is rich. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is not an astronaut.
 From the fact that there is at least one y for which y is an astronaut if and only if y is rich we can infer that there is at least one y for which if y were rich, then y is an astronaut via existential biconditional elimination. Finally, from the fact that there is at least one y for which if y were rich, then y is an astronaut, and that for all y, y is rich we can infer that there is at least one y for which y is an astronaut via existential modus ponens, which contradicts that For all y, y is not an astronaut. Therefore, the answer is no.