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