Consider the following premises. For all x_9, x_9 will not play tennis. There is at least one x_9 for which if x_9 plays tennis, then x_9 is happy. For all x_9, if x_9 were happy, then x_9 is playing tennis. For all x_9, x_9 is happy or x_9 is a politician. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not a politician.
 From the fact that there is at least one x_9 for which if x_9 plays tennis, then x_9 is happy, and that for all x_9, if x_9 were happy, then x_9 is playing tennis we can infer that there is at least one x_9 for which x_9 will play tennis if and only if x_9 is happy via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 will play tennis if and only if x_9 is happy, and that for all x_9, x_9 will not play tennis we can infer that there is at least one x_9 for which x_9 is not happy via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 is happy or x_9 is a politician, and that there is at least one x_9 for which x_9 is not happy we can infer that there is at least one x_9 for which x_9 is a politician via existential disjunctive syllogism, which contradicts that For all x_9, x_9 is not a politician. Therefore, the answer is no.