Consider the following premises. For all z, z is not a politician. For all z, if z were a poet, then z is a politician. For all z, if z were happy, then z is a poet. For all z, if z were a politician, then z is happy. Can we infer the following from them? For all z, z is not a poet.
 From the fact that for all z, if z were a politician, then z is happy, and that for all z, if z were happy, then z is a poet we can infer that for all z, if z were a politician, then z is a poet. From the fact that for all z, if z were a politician, then z is a poet, and that for all z, if z were a poet, then z is a politician we can infer that for all z, z is a politician if and only if z is a poet. Finally, from the fact that for all z, z is a politician if and only if z is a poet, and that for all z, z is not a politician we can infer that for all z, z is not a poet. Therefore, the answer is yes.