Consider the following premises. For all z, z will listen to a song if and only if z is fast. For all z, if z were fast, then z is listening to a song. There is at least one z for which z will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not fast.
 From the fact that for all z, z will listen to a song if and only if z is fast we can infer that for all z, if z listens to a song, then z is fast via universal biconditional elimination. From the fact that for all z, if z listens to a song, then z is fast, and that for all z, if z were fast, then z is listening to a song we can infer that for all z, z will listen to a song if and only if z is fast via universal biconditional introduction. Finally, from the fact that for all z, z will listen to a song if and only if z is fast, and that there is at least one z for which z will not listen to a song we can infer that there is at least one z for which z is not fast via existential biconditional elimination. Therefore, the answer is yes.