Consider the following premises. For all x_10, x_10 will drink water if and only if x_10 is a bartender. Elisabeth is not drinking water. For all x_10, x_10 will drink water if and only if x_10 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is a bartender.
 From the fact that for all x_10, x_10 will drink water if and only if x_10 is a bartender we can infer that for all x_10, if x_10 drinks water, then x_10 is a bartender via universal biconditional elimination. From the fact that for all x_10, x_10 will drink water if and only if x_10 is a bartender we can infer that for all x_10, if x_10 were a bartender, then x_10 is drinking water via universal biconditional elimination. From the fact that for all x_10, if x_10 drinks water, then x_10 is a bartender, and that for all x_10, if x_10 were a bartender, then x_10 is drinking water we can infer that for all x_10, x_10 will drink water if and only if x_10 is a bartender via universal biconditional introduction. From the fact that for all x_10, x_10 will drink water if and only if x_10 is a bartender we can infer that Elisabeth is drinking water if and only if Elisabeth is a bartender via universal instantiation. Finally, from the fact that Elisabeth is drinking water if and only if Elisabeth is a bartender, and that Elisabeth is not drinking water we can infer that Elisabeth is not a bartender via biconditional elimination, which contradicts that Elisabeth is a bartender. Therefore, the answer is no.