Consider the following premises. For all z_1, if z_1 takes a plane, then z_1 is a taxi driver. For all z_1, if z_1 were a taxi driver, then z_1 is taking a plane. There is at least one z_1 for which z_1 will not take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all z_1, z_1 is a taxi driver.
 From the fact that for all z_1, if z_1 takes a plane, then z_1 is a taxi driver, and that for all z_1, if z_1 were a taxi driver, then z_1 is taking a plane we can infer that for all z_1, z_1 will take a plane if and only if z_1 is a taxi driver via universal biconditional introduction. From the fact that for all z_1, z_1 will take a plane if and only if z_1 is a taxi driver we can infer that for all z_1, if z_1 were a taxi driver, then z_1 is taking a plane via universal biconditional elimination. Finally, from the fact that for all z_1, if z_1 were a taxi driver, then z_1 is taking a plane, and that there is at least one z_1 for which z_1 will not take a plane we can infer that there is at least one z_1 for which z_1 is not a taxi driver via existential modus tollens, which contradicts that For all z_1, z_1 is a taxi driver. Therefore, the answer is no.