Consider the following premises. For all x_7, x_7 will not take a plane. For all x_7, x_7 will write a letter if and only if x_7 will take a plane. For all x_7, x_7 will write a letter if and only if x_7 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_7 for which x_7 is a taxi driver.
 From the fact that for all x_7, x_7 will write a letter if and only if x_7 will take a plane we can infer that for all x_7, if x_7 writes a letter, then x_7 is taking a plane via universal biconditional elimination. From the fact that for all x_7, if x_7 writes a letter, then x_7 is taking a plane, and that for all x_7, x_7 will not take a plane we can infer that for all x_7, x_7 will not write a letter via universal modus tollens. Finally, from the fact that for all x_7, x_7 will write a letter if and only if x_7 is a taxi driver, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is not a taxi driver via universal biconditional elimination, which contradicts that There is at least one x_7 for which x_7 is a taxi driver. Therefore, the answer is no.