Consider the following premises. Joseph is driving a car or James is a doctor. If Joseph drives a car, then it is windy. It is raining or James is not a doctor. If it is windy, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that it is raining or James is not a doctor we can infer that if James were a doctor, then it is raining via rewriting. From the fact that if Joseph drives a car, then it is windy, and that if it is windy, then it is raining we can infer that if Joseph drives a car, then it is raining via transitivity. Finally, from the fact that if Joseph drives a car, then it is raining, that if James were a doctor, then it is raining, and that Joseph is driving a car or James is a doctor we can infer that it is raining via disjunction elimination. Therefore, the answer is yes.