Consider the following premises. Mary is curious or Elisabeth is an astronaut. David is driving a car if and only if Elisabeth is an astronaut. David is driving a car or Mary is not curious. Can we infer the following from them? If we can, name the inference rule being used: David is driving a car.
 From the fact that David is driving a car or Mary is not curious we can infer that if Mary were curious, then David is driving a car via rewriting. From the fact that David is driving a car if and only if Elisabeth is an astronaut we can infer that if Elisabeth were an astronaut, then David is driving a car via biconditional elimination. Finally, from the fact that if Mary were curious, then David is driving a car, that if Elisabeth were an astronaut, then David is driving a car, and that Mary is curious or Elisabeth is an astronaut we can infer that David is driving a car via disjunction elimination. Therefore, the answer is yes.