Consider the following premises. It is not raining. If Susan drives a car, then it is raining. Susan is driving a car if and only if David is an astronaut. Can we infer the following from them? David is not an astronaut.
 From the fact that if Susan drives a car, then it is raining, and that it is not raining we can infer that Susan is not driving a car. Finally, from the fact that Susan is driving a car if and only if David is an astronaut, and that Susan is not driving a car we can infer that David is not an astronaut. Therefore, the answer is yes.