Consider the following premises. For all z_3, z_3 is a cashier if and only if z_3 is a taxi driver. For all z_3, z_3 is a cashier or z_3 is not a taxi driver. Can we infer the following from them? There is at least one z_3 for which the fact that z_3 were a cashier does not imply that z_3 is a taxi driver.
 From the fact that for all z_3, z_3 is a cashier if and only if z_3 is a taxi driver we can infer that for all z_3, if z_3 were a cashier, then z_3 is a taxi driver. From the fact that for all z_3, z_3 is a cashier or z_3 is not a taxi driver we can infer that for all z_3, if z_3 were a taxi driver, then z_3 is a cashier. From the fact that for all z_3, if z_3 were a cashier, then z_3 is a taxi driver, and that for all z_3, if z_3 were a taxi driver, then z_3 is a cashier we can infer that for all z_3, z_3 is a cashier if and only if z_3 is a taxi driver. Finally, from the fact that for all z_3, z_3 is a cashier if and only if z_3 is a taxi driver we can infer that for all z_3, if z_3 were a cashier, then z_3 is a taxi driver, which contradicts that There is at least one z_3 for which the fact that z_3 were a cashier does not imply that z_3 is a taxi driver. Therefore, the answer is no.