Consider the following premises. There is at least one z_3 for which z_3 will not work. For all z_3, if z_3 works, then z_3 is playing squash. For all z_3, if z_3 reads a book, then z_3 is working. For all z_3, if z_3 plays squash, then z_3 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_3 for which z_3 will not read a book.
 From the fact that for all z_3, if z_3 works, then z_3 is playing squash, and that for all z_3, if z_3 plays squash, then z_3 is reading a book we can infer that for all z_3, if z_3 works, then z_3 is reading a book via universal transitivity. From the fact that for all z_3, if z_3 works, then z_3 is reading a book, and that for all z_3, if z_3 reads a book, then z_3 is working we can infer that for all z_3, z_3 will work if and only if z_3 will read a book via universal biconditional introduction. Finally, from the fact that for all z_3, z_3 will work if and only if z_3 will read a book, and that there is at least one z_3 for which z_3 will not work we can infer that there is at least one z_3 for which z_3 will not read a book via existential biconditional elimination. Therefore, the answer is yes.