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