Consider the following premises. There is at least one x_7 for which x_7 is rich if and only if x_7 will work. For all x_7, x_7 is a janitor. For all x_7, if x_7 were a janitor, then x_7 is rich. 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 rich.
 From the fact that there is at least one x_7 for which x_7 is rich if and only if x_7 will work we can infer that there is at least one x_7 for which if x_7 works, then x_7 is rich via existential biconditional elimination. From the fact that for all x_7, x_7 is a janitor we can infer that for all x_7, x_7 is a janitor or x_7 will work via universal addition. Finally, from the fact that for all x_7, if x_7 were a janitor, then x_7 is rich, that there is at least one x_7 for which if x_7 works, then x_7 is rich, and that for all x_7, x_7 is a janitor or x_7 will work we can infer that there is at least one x_7 for which x_7 is rich via existential disjunction elimination. Therefore, the answer is yes.