Consider the following premises. Jennifer is sleeping or Barbara is a police officer. If Barbara were a police officer, then it is snowing. If Jennifer sleeps, then it is snowing. If it snows, then Jennifer is sleeping. Can we infer the following from them? It is snowing.
 From the fact that if it snows, then Jennifer is sleeping, and that if Jennifer sleeps, then it is snowing we can infer that it is snowing if and only if Jennifer is sleeping. From the fact that it is snowing if and only if Jennifer is sleeping we can infer that if Jennifer sleeps, then it is snowing. Finally, from the fact that if Jennifer sleeps, then it is snowing, that if Barbara were a police officer, then it is snowing, and that Jennifer is sleeping or Barbara is a police officer we can infer that it is snowing. Therefore, the answer is yes.