Consider the following premises. For all x_9, x_9 will cook if and only if x_9 is a mechanic. For all x_9, x_9 is a server if and only if x_9 will cook. There is at least one x_9 for which if x_9 were a server, then x_9 is rich. For all x_9, x_9 is not rich. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is a mechanic.
 From the fact that there is at least one x_9 for which if x_9 were a server, then x_9 is rich, and that for all x_9, x_9 is not rich we can infer that there is at least one x_9 for which x_9 is not a server via existential modus tollens. From the fact that for all x_9, x_9 is a server if and only if x_9 will cook, and that there is at least one x_9 for which x_9 is not a server we can infer that there is at least one x_9 for which x_9 will not cook via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will cook if and only if x_9 is a mechanic, and that there is at least one x_9 for which x_9 will not cook we can infer that there is at least one x_9 for which x_9 is not a mechanic via existential biconditional elimination, which contradicts that For all x_9, x_9 is a mechanic. Therefore, the answer is no.