Consider the following premises. For all z_3, z_3 is not an astronaut. For all z_3, if z_3 were a janitor, then z_3 is an astronaut. For all z_3, if z_3 were an astronaut, then z_3 is a janitor. Thomas is taking a plane if and only if Michael is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not taking a plane.
 From the fact that for all z_3, if z_3 were a janitor, then z_3 is an astronaut, and that for all z_3, if z_3 were an astronaut, then z_3 is a janitor we can infer that for all z_3, z_3 is a janitor if and only if z_3 is an astronaut via universal biconditional introduction. From the fact that for all z_3, z_3 is a janitor if and only if z_3 is an astronaut, and that for all z_3, z_3 is not an astronaut we can infer that for all z_3, z_3 is not a janitor via universal biconditional elimination. From the fact that for all z_3, z_3 is not a janitor we can infer that Michael is not a janitor via universal instantiation. Finally, from the fact that Thomas is taking a plane if and only if Michael is a janitor, and that Michael is not a janitor we can infer that Thomas is not taking a plane via biconditional elimination. Therefore, the answer is yes.