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