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