Consider the following premises. For all y, y will read a book or y is not fast. For all y, y will read a book if and only if y is fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which if is not true that y is fast if and only if y will read a book.
 From the fact that for all y, y will read a book or y is not fast we can infer that for all y, if y were fast, then y is reading a book via universal rewriting. From the fact that for all y, y will read a book if and only if y is fast we can infer that for all y, if y reads a book, then y is fast via universal biconditional elimination. Finally, from the fact that for all y, if y were fast, then y is reading a book, and that for all y, if y reads a book, then y is fast we can infer that for all y, y is fast if and only if y will read a book via universal biconditional introduction, which contradicts that There is at least one y for which if is not true that y is fast if and only if y will read a book. Therefore, the answer is no.