Consider the following premises. There is at least one y_2 for which y_2 will go running if and only if y_2 is fast. For all y_2, if y_2 were fast, then y_2 is a taxi driver. For all y_2, y_2 will go running or y_2 is not a taxi driver. Can we infer the following from them? There is at least one y_2 for which y_2 is fast if and only if y_2 will go running.
 From the fact that for all y_2, y_2 will go running or y_2 is not a taxi driver we can infer that for all y_2, if y_2 were a taxi driver, then y_2 is running. From the fact that for all y_2, if y_2 were fast, then y_2 is a taxi driver, and that for all y_2, if y_2 were a taxi driver, then y_2 is running we can infer that for all y_2, if y_2 were fast, then y_2 is running. From the fact that there is at least one y_2 for which y_2 will go running if and only if y_2 is fast we can infer that there is at least one y_2 for which if y_2 goes running, then y_2 is fast. Finally, from the fact that for all y_2, if y_2 were fast, then y_2 is running, and that there is at least one y_2 for which if y_2 goes running, then y_2 is fast we can infer that there is at least one y_2 for which y_2 is fast if and only if y_2 will go running. Therefore, the answer is yes.