Consider the following premises. For all z, z will drive a car or z will not play squash. There is at least one z for which z will not play squash. For all z, z will play squash or z will not drive a car. 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 will not drive a car.
 From the fact that for all z, z will drive a car or z will not play squash we can infer that for all z, if z plays squash, then z is driving a car via universal rewriting. From the fact that for all z, z will play squash or z will not drive a car we can infer that for all z, if z drives a car, then z is playing squash via universal rewriting. From the fact that for all z, if z plays squash, then z is driving a car, and that for all z, if z drives a car, then z is playing squash we can infer that for all z, z will play squash if and only if z will drive a car via universal biconditional introduction. Finally, from the fact that for all z, z will play squash if and only if z will drive a car, and that there is at least one z for which z will not play squash we can infer that there is at least one z for which z will not drive a car via existential biconditional elimination. Therefore, the answer is yes.