Consider the following premises. For all y, y is happy if and only if y is rich. For all y, y is happy or y will read a book. For all y, y will not work. For all y, y will work if and only if y is rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will not read a book.
 From the fact that for all y, y will work if and only if y is rich, and that for all y, y will not work we can infer that for all y, y is not rich via universal biconditional elimination. From the fact that for all y, y is happy if and only if y is rich, and that for all y, y is not rich we can infer that for all y, y is not happy via universal biconditional elimination. Finally, from the fact that for all y, y is happy or y will read a book, and that for all y, y is not happy we can infer that for all y, y will read a book via universal disjunctive syllogism, which contradicts that There is at least one y for which y will not read a book. Therefore, the answer is no.