Consider the following premises. For all y, if y sleeps, then y is bored. For all y, y will not sleep. For all y, if y were bored, then y is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is not bored.
 From the fact that for all y, if y were bored, then y is sleeping, and that for all y, if y sleeps, then y is bored we can infer that for all y, y is bored if and only if y will sleep via universal biconditional introduction. From the fact that for all y, y is bored if and only if y will sleep we can infer that for all y, if y were bored, then y is sleeping via universal biconditional elimination. Finally, from the fact that for all y, if y were bored, then y is sleeping, and that for all y, y will not sleep we can infer that for all y, y is not bored via universal modus tollens. Therefore, the answer is yes.