Consider the following premises. For all z, z is rich or z will not read a book. For all z, if z were rich, then z is reading a book. There is at least one z for which z will not read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not rich.
 From the fact that for all z, z is rich or z will not read a book we can infer that for all z, if z reads a book, then z is rich via universal rewriting. From the fact that for all z, if z were rich, then z is reading a book, and that for all z, if z reads a book, then z is rich we can infer that for all z, z is rich if and only if z will read a book via universal biconditional introduction. Finally, from the fact that for all z, z is rich if and only if z will read a book, and that there is at least one z for which z will not read a book we can infer that there is at least one z for which z is not rich via existential biconditional elimination. Therefore, the answer is yes.