Consider the following premises. For all x_10, x_10 is a janitor and x_10 will play tennis. For all x_10, if x_10 were a janitor, then x_10 is fast. There is at least one x_10 for which if x_10 were fast, then x_10 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is fast.
 From the fact that for all x_10, x_10 is a janitor and x_10 will play tennis we can infer that for all x_10, x_10 is a janitor via universal simplification. From the fact that there is at least one x_10 for which if x_10 were fast, then x_10 is a janitor, and that for all x_10, if x_10 were a janitor, then x_10 is fast we can infer that there is at least one x_10 for which x_10 is fast if and only if x_10 is a janitor via existential biconditional introduction. From the fact that there is at least one x_10 for which x_10 is fast if and only if x_10 is a janitor we can infer that there is at least one x_10 for which if x_10 were a janitor, then x_10 is fast via existential biconditional elimination. Finally, from the fact that there is at least one x_10 for which if x_10 were a janitor, then x_10 is fast, and that for all x_10, x_10 is a janitor we can infer that there is at least one x_10 for which x_10 is fast via existential modus ponens. Therefore, the answer is yes.