Consider the following premises. There is at least one x for which x will drive a car or x will not work. For all x, x will drive a car if and only if x will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will work if and only if x will drive a car.
 From the fact that for all x, x will drive a car if and only if x will work we can infer that for all x, if x drives a car, then x is working via universal biconditional elimination. From the fact that there is at least one x for which x will drive a car or x will not work we can infer that there is at least one x for which if x works, then x is driving a car via existential rewriting. Finally, from the fact that there is at least one x for which if x works, then x is driving a car, and that for all x, if x drives a car, then x is working we can infer that there is at least one x for which x will work if and only if x will drive a car via existential biconditional introduction. Therefore, the answer is yes.