Consider the following premises. For all x_7, x_7 is a politician. For all x_7, if x_7 were a politician, then x_7 is sleeping. For all x_7, x_7 will sleep if and only if x_7 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will not drink water.
 From the fact that for all x_7, x_7 will sleep if and only if x_7 will drink water we can infer that for all x_7, if x_7 sleeps, then x_7 is drinking water via universal biconditional elimination. From the fact that for all x_7, if x_7 were a politician, then x_7 is sleeping, and that for all x_7, x_7 is a politician we can infer that for all x_7, x_7 will sleep via universal modus ponens. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is drinking water, and that for all x_7, x_7 will sleep we can infer that for all x_7, x_7 will drink water via universal modus ponens, which contradicts that There is at least one x_7 for which x_7 will not drink water. Therefore, the answer is no.