Consider the following premises. For all y, y will not take a plane. There is at least one y for which if y were bored, then y is a janitor. For all y, y will take a plane if and only if y is bored. For all y, if y were a janitor, then y is bored. 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 a janitor.
 From the fact that for all y, if y were a janitor, then y is bored, and that there is at least one y for which if y were bored, then y is a janitor we can infer that there is at least one y for which y is a janitor if and only if y is bored via existential biconditional introduction. From the fact that for all y, y will take a plane if and only if y is bored, and that for all y, y will not take a plane we can infer that for all y, y is not bored via universal biconditional elimination. Finally, from the fact that there is at least one y for which y is a janitor if and only if y is bored, and that for all y, y is not bored we can infer that there is at least one y for which y is not a janitor via existential biconditional elimination. Therefore, the answer is yes.