Consider the following premises. For all z, z is a writer or z will not sleep. For all z, z is a writer if and only if z will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all z, if z sleeps, then z is a writer.
 From the fact that for all z, z is a writer if and only if z will sleep we can infer that for all z, if z were a writer, then z is sleeping via universal biconditional elimination. Finally, from the fact that for all z, z is a writer or z will not sleep we can infer that for all z, if z sleeps, then z is a writer via universal rewriting. Therefore, the answer is yes.