Consider the following premises. There is at least one x_5 for which if x_5 works, then x_5 is driving a car. For all x_5, x_5 will work. For all x_5, x_5 is a taxi driver if and only if x_5 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not drive a car.
 From the fact that for all x_5, x_5 will work we can infer that for all x_5, x_5 will work or x_5 is a taxi driver via universal addition. From the fact that for all x_5, x_5 is a taxi driver if and only if x_5 will drive a car we can infer that for all x_5, if x_5 were a taxi driver, then x_5 is driving a car via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which if x_5 works, then x_5 is driving a car, that for all x_5, if x_5 were a taxi driver, then x_5 is driving a car, and that for all x_5, x_5 will work or x_5 is a taxi driver we can infer that there is at least one x_5 for which x_5 will drive a car via existential disjunction elimination, which contradicts that For all x_5, x_5 will not drive a car. Therefore, the answer is no.