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