Consider the following premises. It is cloudy. If it is cloudy, then it is cold. It is cold or Jessica is not fast. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that it is cold or Jessica is not fast we can infer that if Jessica were fast, then it is cold via rewriting. From the fact that it is cloudy we can infer that it is cloudy or Jessica is fast via addition. Finally, from the fact that if it is cloudy, then it is cold, that if Jessica were fast, then it is cold, and that it is cloudy or Jessica is fast we can infer that it is cold via disjunction elimination. Therefore, the answer is yes.