Consider the following premises. There is at least one x_7 for which if x_7 were curious, then x_7 is a bartender. For all x_7, x_7 is curious. For all x_7, if x_7 were a bartender, then x_7 is curious. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not a bartender.
 From the fact that for all x_7, if x_7 were a bartender, then x_7 is curious, and that there is at least one x_7 for which if x_7 were curious, then x_7 is a bartender we can infer that there is at least one x_7 for which x_7 is a bartender if and only if x_7 is curious via existential biconditional introduction. From the fact that there is at least one x_7 for which x_7 is a bartender if and only if x_7 is curious we can infer that there is at least one x_7 for which if x_7 were curious, then x_7 is a bartender via existential biconditional elimination. Finally, from the fact that there is at least one x_7 for which if x_7 were curious, then x_7 is a bartender, and that for all x_7, x_7 is curious we can infer that there is at least one x_7 for which x_7 is a bartender via existential modus ponens, which contradicts that For all x_7, x_7 is not a bartender. Therefore, the answer is no.