Consider the following premises. For all z, z will make tea if and only if z will sleep. There is at least one z for which if z sleeps, then z is listening to a song. For all z, if z listens to a song, then z is making tea. Can we infer the following from them? There is at least one z for which z will make tea if and only if z will listen to a song.
 From the fact that for all z, z will make tea if and only if z will sleep we can infer that for all z, if z makes tea, then z is sleeping. From the fact that for all z, if z makes tea, then z is sleeping, and that there is at least one z for which if z sleeps, then z is listening to a song we can infer that there is at least one z for which if z makes tea, then z is listening to a song. Finally, from the fact that there is at least one z for which if z makes tea, then z is listening to a song, and that for all z, if z listens to a song, then z is making tea we can infer that there is at least one z for which z will make tea if and only if z will listen to a song. Therefore, the answer is yes.