Consider the following premises. For all y, if y takes a plane, then y is bored. For all y, y is bored if and only if y will take a plane. For all y, y will not take a plane. 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 bored.
 From the fact that for all y, y is bored if and only if y will take a plane we can infer that for all y, if y were bored, then y is taking a plane via universal biconditional elimination. From the fact that for all y, if y takes a plane, then y is bored, and that for all y, if y were bored, then y is taking a plane we can infer that for all y, y will take a plane if and only if y is bored via universal biconditional introduction. Finally, 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, which contradicts that There is at least one y for which y is bored. Therefore, the answer is no.