Consider the following premises. For all z, z will sleep or z is not a mechanic. For all z, if z sleeps, then z is driving a car. 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: There is at least one z for which if is not true that z will drive a car if and only if z is a mechanic.
 From the fact that for all z, z will sleep or z is not a mechanic we can infer that for all z, if z were a mechanic, then z is sleeping via universal rewriting. From the fact that for all z, if z were a mechanic, then z is sleeping, and that for all z, if z sleeps, then z is driving a car we can infer that for all z, if z were a mechanic, then z is driving a car via universal transitivity. Finally, from the fact that for all z, if z drives a car, then z is a mechanic, and that for all z, if z were a mechanic, then z is driving a car we can infer that for all z, z will drive a car if and only if z is a mechanic via universal biconditional introduction, which contradicts that There is at least one z for which if is not true that z will drive a car if and only if z is a mechanic. Therefore, the answer is no.