Consider the following premises. For all x_9, x_9 is not a cashier. For all x_9, x_9 will play tennis if and only if x_9 will make tea. For all x_9, if x_9 plays tennis, then x_9 is a cashier. For all x_9, if x_9 were rich, then x_9 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not rich.
 From the fact that for all x_9, if x_9 plays tennis, then x_9 is a cashier, and that for all x_9, x_9 is not a cashier we can infer that for all x_9, x_9 will not play tennis via universal modus tollens. From the fact that for all x_9, x_9 will play tennis if and only if x_9 will make tea we can infer that for all x_9, if x_9 makes tea, then x_9 is playing tennis via universal biconditional elimination. From the fact that for all x_9, if x_9 were rich, then x_9 is making tea, and that for all x_9, if x_9 makes tea, then x_9 is playing tennis we can infer that for all x_9, if x_9 were rich, then x_9 is playing tennis via universal transitivity. Finally, from the fact that for all x_9, if x_9 were rich, then x_9 is playing tennis, and that for all x_9, x_9 will not play tennis we can infer that for all x_9, x_9 is not rich via universal modus tollens. Therefore, the answer is yes.