Consider the following premises. There is at least one z_2 for which if z_2 makes tea, then z_2 is working. For all z_2, z_2 will not drive a car. For all z_2, if z_2 works, then z_2 is making tea. For all z_2, z_2 will make tea if and only if z_2 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all z_2, z_2 will work.
 From the fact that for all z_2, if z_2 works, then z_2 is making tea, and that there is at least one z_2 for which if z_2 makes tea, then z_2 is working we can infer that there is at least one z_2 for which z_2 will work if and only if z_2 will make tea via existential biconditional introduction. From the fact that for all z_2, z_2 will make tea if and only if z_2 will drive a car, and that for all z_2, z_2 will not drive a car we can infer that for all z_2, z_2 will not make tea via universal biconditional elimination. Finally, from the fact that there is at least one z_2 for which z_2 will work if and only if z_2 will make tea, and that for all z_2, z_2 will not make tea we can infer that there is at least one z_2 for which z_2 will not work via existential biconditional elimination, which contradicts that For all z_2, z_2 will work. Therefore, the answer is no.