Consider the following premises. There is at least one z for which if z writes a letter, then z is sleeping. For all z, z will not sleep. For all z, if z were rich, then z is writing a letter. Can we infer the following from them? For all z, z is rich.
 From the fact that there is at least one z for which if z writes a letter, then z is sleeping, and that for all z, z will not sleep we can infer that there is at least one z for which z will not write a letter. Finally, from the fact that for all z, if z were rich, then z is writing a letter, and that there is at least one z for which z will not write a letter we can infer that there is at least one z for which z is not rich, which contradicts that For all z, z is rich. Therefore, the answer is no.