Consider the following premises. For all x_9, if x_9 were happy, then x_9 is a janitor. For all x_9, x_9 is happy or x_9 is not poor. For all x_9, if x_9 were a janitor, then x_9 is a taxi driver. For all x_9, if x_9 were a taxi driver, then x_9 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is a taxi driver if and only if x_9 is happy.
 From the fact that for all x_9, if x_9 were happy, then x_9 is a janitor, and that for all x_9, if x_9 were a janitor, then x_9 is a taxi driver we can infer that for all x_9, if x_9 were happy, then x_9 is a taxi driver via universal transitivity. From the fact that for all x_9, x_9 is happy or x_9 is not poor we can infer that for all x_9, if x_9 were poor, then x_9 is happy via universal rewriting. From the fact that for all x_9, if x_9 were a taxi driver, then x_9 is poor, and that for all x_9, if x_9 were poor, then x_9 is happy we can infer that for all x_9, if x_9 were a taxi driver, then x_9 is happy via universal transitivity. Finally, from the fact that for all x_9, if x_9 were a taxi driver, then x_9 is happy, and that for all x_9, if x_9 were happy, then x_9 is a taxi driver we can infer that for all x_9, x_9 is a taxi driver if and only if x_9 is happy via universal biconditional introduction. Therefore, the answer is yes.