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