Consider the following premises. For all z, if z drives a car, then z is fast. For all z, if z were fast, then z is a taxi driver. For all z, if z were a taxi driver, then z is driving a car. There is at least one z for which if z were a taxi driver, then z is fast. Can we infer the following from them? There is at least one z for which z is fast if and only if z is a taxi driver.
Yes.