Consider the following premises. For all x_5, if x_5 drinks water, then x_5 is a politician. For all x_5, x_5 is not rich. For all x_5, x_5 will drink water if and only if x_5 is rich. There is at least one x_5 for which if x_5 were a politician, then x_5 is drinking water. Can we infer the following from them? There is at least one x_5 for which x_5 is not a politician.
 From the fact that there is at least one x_5 for which if x_5 were a politician, then x_5 is drinking water, and that for all x_5, if x_5 drinks water, then x_5 is a politician we can infer that there is at least one x_5 for which x_5 is a politician if and only if x_5 will drink water. From the fact that for all x_5, x_5 will drink water if and only if x_5 is rich, and that for all x_5, x_5 is not rich we can infer that for all x_5, x_5 will not drink water. Finally, from the fact that there is at least one x_5 for which x_5 is a politician if and only if x_5 will drink water, and that for all x_5, x_5 will not drink water we can infer that there is at least one x_5 for which x_5 is not a politician. Therefore, the answer is yes.