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