Consider the following premises. For all y, y is a taxi driver or y is not a politician. There is at least one y for which y is a politician or y is not a taxi driver. Can we infer the following from them? For all y, if is not true that y is a politician if and only if y is a taxi driver.
 From the fact that for all y, y is a taxi driver or y is not a politician we can infer that for all y, if y were a politician, then y is a taxi driver. From the fact that there is at least one y for which y is a politician or y is not a taxi driver we can infer that there is at least one y for which if y were a taxi driver, then y is a politician. Finally, from the fact that for all y, if y were a politician, then y is a taxi driver, and that there is at least one y for which if y were a taxi driver, then y is a politician we can infer that there is at least one y for which y is a politician if and only if y is a taxi driver, which contradicts that For all y, if is not true that y is a politician if and only if y is a taxi driver. Therefore, the answer is no.