Consider the following premises. David is not driving a car. It is late or Michael is rich. It is not late or it is raining. David is driving a car if and only if Michael is rich. Can we infer the following from them? It is raining.
 From the fact that David is driving a car if and only if Michael is rich, and that David is not driving a car we can infer that Michael is not rich. From the fact that it is late or Michael is rich, and that it is not late or it is raining we can infer that Michael is rich or it is raining. Finally, from the fact that Michael is rich or it is raining, and that Michael is not rich we can infer that it is raining. Therefore, the answer is yes.