Consider the following premises. Michael is rich. If Michael were rich, then it is overcast. For all y, y is a soldier. Can we infer the following from them? It is overcast.
 From the fact that for all y, y is a soldier we can infer that John is a soldier. From the fact that Michael is rich, and that John is a soldier we can infer that Michael is rich and John is a soldier. From the fact that Michael is rich and John is a soldier we can infer that Michael is rich. Finally, from the fact that if Michael were rich, then it is overcast, and that Michael is rich we can infer that it is overcast. Therefore, the answer is yes.