Consider the following premises. For all x_5, if x_5 were a soldier, then x_5 is not poor. For all x_5, x_5 is poor. For all x_5, if x_5 were a taxi driver, then x_5 is a soldier. For all x_5, if x_5 were a soldier, then x_5 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not a taxi driver.
 From the fact that for all x_5, if x_5 were a soldier, then x_5 is a taxi driver, and that for all x_5, if x_5 were a taxi driver, then x_5 is a soldier we can infer that for all x_5, x_5 is a soldier if and only if x_5 is a taxi driver via universal biconditional introduction. From the fact that for all x_5, if x_5 were a soldier, then x_5 is not poor, and that for all x_5, x_5 is poor we can infer that for all x_5, x_5 is not a soldier via universal modus tollens. Finally, from the fact that for all x_5, x_5 is a soldier if and only if x_5 is a taxi driver, and that for all x_5, x_5 is not a soldier we can infer that for all x_5, x_5 is not a taxi driver via universal biconditional elimination. Therefore, the answer is yes.