Consider the following premises. For all y, y will work if and only if y will play a game. For all y, y will play a game or y is not an office clerk. There is at least one y for which y will not work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is not an office clerk.
 From the fact that for all y, y will work if and only if y will play a game, and that there is at least one y for which y will not work we can infer that there is at least one y for which y will not play a game via existential biconditional elimination. From the fact that for all y, y will play a game or y is not an office clerk we can infer that for all y, if y were an office clerk, then y is playing a game via universal rewriting. Finally, from the fact that for all y, if y were an office clerk, then y is playing a game, and that there is at least one y for which y will not play a game we can infer that there is at least one y for which y is not an office clerk via existential modus tollens. Therefore, the answer is yes.