Consider the following premises. It is cloudy if and only if Thomas is a police officer. It is cold if and only if Thomas is a police officer. It is not cold. If Thomas were a police officer, then it is cloudy. Can we infer the following from them? It is not cloudy.
 From the fact that it is cloudy if and only if Thomas is a police officer we can infer that if it is cloudy, then Thomas is a police officer. From the fact that if it is cloudy, then Thomas is a police officer, and that if Thomas were a police officer, then it is cloudy we can infer that it is cloudy if and only if Thomas is a police officer. From the fact that it is cold if and only if Thomas is a police officer, and that it is not cold we can infer that Thomas is not a police officer. Finally, from the fact that it is cloudy if and only if Thomas is a police officer, and that Thomas is not a police officer we can infer that it is not cloudy. Therefore, the answer is yes.