Consider the following premises. For all x, if x were fast, then x is driving a car. There is at least one x for which x is not a mechanic. For all x, if x drives a car, then x is fast. For all x, if x were fast, then x is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will drive a car.
 From the fact that for all x, if x were fast, then x is driving a car, and that for all x, if x drives a car, then x is fast we can infer that for all x, x is fast if and only if x will drive a car via universal biconditional introduction. From the fact that for all x, if x were fast, then x is a mechanic, and that there is at least one x for which x is not a mechanic we can infer that there is at least one x for which x is not fast via existential modus tollens. Finally, from the fact that for all x, x is fast if and only if x will drive a car, and that there is at least one x for which x is not fast we can infer that there is at least one x for which x will not drive a car via existential biconditional elimination, which contradicts that For all x, x will drive a car. Therefore, the answer is no.