Consider the following premises. There is at least one x_9 for which x_9 is rich if and only if x_9 is bored. For all x_9, x_9 is a bartender. For all x_9, if x_9 were a bartender, then x_9 is bored. 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 there is at least one x_9 for which x_9 is rich if and only if x_9 is bored we can infer that there is at least one x_9 for which if x_9 were bored, then x_9 is rich via existential biconditional elimination. From the fact that for all x_9, if x_9 were a bartender, then x_9 is bored, and that for all x_9, x_9 is a bartender we can infer that for all x_9, x_9 is bored via universal modus ponens. Finally, from the fact that there is at least one x_9 for which if x_9 were bored, then x_9 is rich, and that for all x_9, x_9 is bored we can infer that there is at least one x_9 for which x_9 is rich via existential modus ponens, which contradicts that For all x_9, x_9 is not rich. Therefore, the answer is no.