Consider the following premises. For all z, z is a writer if and only if z will take a plane. There is at least one z for which z will take a plane if and only if z will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all z, the fact that z listens to a song does not imply that z is a writer.
 From the fact that there is at least one z for which z will take a plane if and only if z will listen to a song we can infer that there is at least one z for which if z listens to a song, then z is taking a plane via existential biconditional elimination. Finally, from the fact that for all z, z is a writer if and only if z will take a plane we can infer that for all z, if z takes a plane, then z is a writer via universal biconditional elimination, which contradicts that For all z, the fact that z listens to a song does not imply that z is a writer. Therefore, the answer is no.