Consider the following premises. For all x_9, x_9 will take a plane if and only if x_9 is poor. For all x_9, x_9 will write a letter. For all x_9, if x_9 were a taxi driver, then x_9 is taking a plane. For all x_9, if x_9 writes a letter, then x_9 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is not poor.
 From the fact that for all x_9, if x_9 writes a letter, then x_9 is a taxi driver, and that for all x_9, if x_9 were a taxi driver, then x_9 is taking a plane we can infer that for all x_9, if x_9 writes a letter, then x_9 is taking a plane via universal transitivity. From the fact that for all x_9, x_9 will take a plane if and only if x_9 is poor we can infer that for all x_9, if x_9 takes a plane, then x_9 is poor via universal biconditional elimination. From the fact that for all x_9, if x_9 writes a letter, then x_9 is taking a plane, and that for all x_9, x_9 will write a letter we can infer that for all x_9, x_9 will take a plane via universal modus ponens. Finally, from the fact that for all x_9, if x_9 takes a plane, then x_9 is poor, and that for all x_9, x_9 will take a plane we can infer that for all x_9, x_9 is poor via universal modus ponens, which contradicts that There is at least one x_9 for which x_9 is not poor. Therefore, the answer is no.