Consider the following premises. For all y, if y plays a game, then y is sad. For all y, if y were sad, then y is playing a game. For all y, y will not play a game. There is at least one y for which y is sad if and only if y is an office clerk. 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, if y plays a game, then y is sad, and that for all y, if y were sad, then y is playing a game we can infer that for all y, y will play a game if and only if y is sad via universal biconditional introduction. From the fact that for all y, y will play a game if and only if y is sad, and that for all y, y will not play a game we can infer that for all y, y is not sad via universal biconditional elimination. Finally, from the fact that there is at least one y for which y is sad if and only if y is an office clerk, and that for all y, y is not sad we can infer that there is at least one y for which y is not an office clerk via existential biconditional elimination. Therefore, the answer is yes.