Consider the following premises. For all z_1, if z_1 plays squash, then z_1 is rich. For all z_1, if z_1 were rich, then z_1 is playing squash. There is at least one z_1 for which z_1 will not play squash. For all z_1, if z_1 were rich, then z_1 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which z_1 is not rich.
 From the fact that for all z_1, if z_1 were rich, then z_1 is playing squash, and that for all z_1, if z_1 plays squash, then z_1 is rich we can infer that for all z_1, z_1 is rich if and only if z_1 will play squash via universal biconditional introduction. From the fact that for all z_1, z_1 is rich if and only if z_1 will play squash we can infer that for all z_1, if z_1 plays squash, then z_1 is rich via universal biconditional elimination. From the fact that for all z_1, if z_1 were rich, then z_1 is playing squash, and that for all z_1, if z_1 plays squash, then z_1 is rich we can infer that for all z_1, z_1 is rich if and only if z_1 will play squash via universal biconditional introduction. Finally, from the fact that for all z_1, z_1 is rich if and only if z_1 will play squash, and that there is at least one z_1 for which z_1 will not play squash we can infer that there is at least one z_1 for which z_1 is not rich via existential biconditional elimination. Therefore, the answer is yes.