Consider the following premises. John is rich if and only if Richard is a nurse. It is not overcast. If Richard were a nurse, then it is cold. If John were rich, then it is overcast. If it is cold, then Richard is a nurse. Can we infer the following from them? It is not cold.
 From the fact that if Richard were a nurse, then it is cold, and that if it is cold, then Richard is a nurse we can infer that Richard is a nurse if and only if it is cold. From the fact that if John were rich, then it is overcast, and that it is not overcast we can infer that John is not rich. From the fact that John is rich if and only if Richard is a nurse, and that John is not rich we can infer that Richard is not a nurse. Finally, from the fact that Richard is a nurse if and only if it is cold, and that Richard is not a nurse we can infer that it is not cold. Therefore, the answer is yes.