Consider the following premises. For all x_7, x_7 is a politician or x_7 will not work. There is at least one x_7 for which x_7 will work or x_7 is not a taxi driver. 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 if x_7 were a taxi driver, then x_7 is a politician.
 From the fact that for all x_7, x_7 is a politician or x_7 will not work we can infer that for all x_7, if x_7 works, then x_7 is a politician via universal rewriting. From the fact that there is at least one x_7 for which x_7 will work or x_7 is not a taxi driver we can infer that there is at least one x_7 for which if x_7 were a taxi driver, then x_7 is working via existential rewriting. Finally, from the fact that there is at least one x_7 for which if x_7 were a taxi driver, then x_7 is working, and that for all x_7, if x_7 works, then x_7 is a politician we can infer that there is at least one x_7 for which if x_7 were a taxi driver, then x_7 is a politician via existential transitivity. Therefore, the answer is yes.