Consider the following premises. For all z, if z were a mechanic, then z is taking a plane. There is at least one z for which if z takes a plane, then z is driving a car. For all z, z is not a mechanic. For all z, if z drives a car, then z is a mechanic. 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 there is at least one z for which if z takes a plane, then z is driving a car, and that for all z, if z drives a car, then z is a mechanic we can infer that there is at least one z for which if z takes a plane, then z is a mechanic via existential transitivity. From the fact that there is at least one z for which if z takes a plane, then z is a mechanic, and that for all z, if z were a mechanic, 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 a mechanic 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 a mechanic, and that for all z, z is not a mechanic 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.