Consider the following premises. Elisabeth is a lawyer or William is not driving a car. If it is cold, then William is driving a car. If it rains, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: If it rains, then Elisabeth is a lawyer.
 From the fact that Elisabeth is a lawyer or William is not driving a car we can infer that if William drives a car, then Elisabeth is a lawyer via rewriting. From the fact that if it is cold, then William is driving a car, and that if William drives a car, then Elisabeth is a lawyer we can infer that if it is cold, then Elisabeth is a lawyer via transitivity. Finally, from the fact that if it rains, then it is cold, and that if it is cold, then Elisabeth is a lawyer we can infer that if it rains, then Elisabeth is a lawyer via transitivity. Therefore, the answer is yes.