Consider the following premises. For all x_7, x_7 is a taxi driver or x_7 is not rich. There is at least one x_7 for which if x_7 were a taxi driver, then x_7 is an office clerk. For all x_7, if x_7 were an office clerk, then x_7 is a carpenter. Can we infer the following from them? There is at least one x_7 for which if x_7 were rich, then x_7 is a carpenter.
 From the fact that for all x_7, x_7 is a taxi driver or x_7 is not rich we can infer that for all x_7, if x_7 were rich, then x_7 is a taxi driver. From the fact that for all x_7, if x_7 were rich, then x_7 is a taxi driver, and that there is at least one x_7 for which if x_7 were a taxi driver, then x_7 is an office clerk we can infer that there is at least one x_7 for which if x_7 were rich, then x_7 is an office clerk. Finally, from the fact that there is at least one x_7 for which if x_7 were rich, then x_7 is an office clerk, and that for all x_7, if x_7 were an office clerk, then x_7 is a carpenter we can infer that there is at least one x_7 for which if x_7 were rich, then x_7 is a carpenter. Therefore, the answer is yes.