Consider the following premises. There is at least one y for which y is fast if and only if y will work. For all y, if y takes a plane, then y is working. For all y, if y were fast, then y is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all y, if is not true that y will work if and only if y is fast.
 From the fact that there is at least one y for which y is fast if and only if y will work we can infer that there is at least one y for which if y works, then y is fast via existential biconditional elimination. From the fact that for all y, if y were fast, then y is taking a plane, and that for all y, if y takes a plane, then y is working we can infer that for all y, if y were fast, then y is working via universal transitivity. Finally, from the fact that there is at least one y for which if y works, then y is fast, and that for all y, if y were fast, then y is working we can infer that there is at least one y for which y will work if and only if y is fast via existential biconditional introduction, which contradicts that For all y, if is not true that y will work if and only if y is fast. Therefore, the answer is no.