Consider the following premises. For all x_7, x_7 is a politician or x_7 will work. For all x_7, x_7 will not drink water. There is at least one x_7 for which x_7 is a politician if and only if x_7 will drink water. Can we infer the following from them? There is at least one x_7 for which x_7 will work.
 From the fact that there is at least one x_7 for which x_7 is a politician if and only if x_7 will drink water, and that for all x_7, x_7 will not drink water we can infer that there is at least one x_7 for which x_7 is not a politician. Finally, from the fact that for all x_7, x_7 is a politician or x_7 will work, and that there is at least one x_7 for which x_7 is not a politician we can infer that there is at least one x_7 for which x_7 will work. Therefore, the answer is yes.