Consider the following premises. For all x_2, x_2 is not a bartender. For all x_2, if x_2 were a taxi driver, then x_2 is a mechanic. For all x_2, if x_2 were a mechanic, then x_2 is a taxi driver. For all x_2, x_2 is a bartender if and only if x_2 is a taxi driver. Can we infer the following from them? There is at least one x_2 for which x_2 is a mechanic.
 From the fact that for all x_2, x_2 is a bartender if and only if x_2 is a taxi driver, and that for all x_2, x_2 is not a bartender we can infer that for all x_2, x_2 is not a taxi driver. From the fact that for all x_2, if x_2 were a taxi driver, then x_2 is a mechanic, and that for all x_2, if x_2 were a mechanic, then x_2 is a taxi driver we can infer that for all x_2, x_2 is a taxi driver if and only if x_2 is a mechanic. Finally, from the fact that for all x_2, x_2 is a taxi driver if and only if x_2 is a mechanic, and that for all x_2, x_2 is not a taxi driver we can infer that for all x_2, x_2 is not a mechanic, which contradicts that There is at least one x_2 for which x_2 is a mechanic. Therefore, the answer is no.