Consider the following premises. For all x_12, if x_12 writes a letter, then x_12 is a taxi driver. There is at least one x_12 for which x_12 is a mechanic if and only if x_12 is a bartender. For all x_12, x_12 is a bartender or x_12 is not a taxi driver. Can we infer the following from them? There is at least one x_12 for which if x_12 writes a letter, then x_12 is a mechanic.
 From the fact that for all x_12, x_12 is a bartender or x_12 is not a taxi driver we can infer that for all x_12, if x_12 were a taxi driver, then x_12 is a bartender. From the fact that there is at least one x_12 for which x_12 is a mechanic if and only if x_12 is a bartender we can infer that there is at least one x_12 for which if x_12 were a bartender, then x_12 is a mechanic. From the fact that for all x_12, if x_12 were a taxi driver, then x_12 is a bartender, and that there is at least one x_12 for which if x_12 were a bartender, then x_12 is a mechanic we can infer that there is at least one x_12 for which if x_12 were a taxi driver, then x_12 is a mechanic. Finally, from the fact that for all x_12, if x_12 writes a letter, then x_12 is a taxi driver, and that there is at least one x_12 for which if x_12 were a taxi driver, then x_12 is a mechanic we can infer that there is at least one x_12 for which if x_12 writes a letter, then x_12 is a mechanic. Therefore, the answer is yes.