Consider the following premises. For all x_10, x_10 is excited. For all x_10, if x_10 sleeps, then x_10 is not excited. There is at least one x_10 for which x_10 will take a plane if and only if x_10 will sleep. For all x_10, x_10 is rich if and only if x_10 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is not rich.
 From the fact that for all x_10, if x_10 sleeps, then x_10 is not excited, and that for all x_10, x_10 is excited we can infer that for all x_10, x_10 will not sleep via universal modus tollens. From the fact that there is at least one x_10 for which x_10 will take a plane if and only if x_10 will sleep, and that for all x_10, x_10 will not sleep we can infer that there is at least one x_10 for which x_10 will not take a plane via existential biconditional elimination. Finally, from the fact that for all x_10, x_10 is rich if and only if x_10 will take a plane, and that there is at least one x_10 for which x_10 will not take a plane we can infer that there is at least one x_10 for which x_10 is not rich via existential biconditional elimination. Therefore, the answer is yes.