Consider the following premises. For all y_2, y_2 will listen to a song or y_2 will not sleep. There is at least one y_2 for which y_2 will sleep if and only if y_2 will listen to a song. Can we infer the following from them? There is at least one y_2 for which if y_2 sleeps, then y_2 is listening to a song.
 From the fact that there is at least one y_2 for which y_2 will sleep if and only if y_2 will listen to a song we can infer that there is at least one y_2 for which if y_2 listens to a song, then y_2 is sleeping. From the fact that for all y_2, y_2 will listen to a song or y_2 will not sleep we can infer that for all y_2, if y_2 sleeps, then y_2 is listening to a song. From the fact that for all y_2, if y_2 sleeps, then y_2 is listening to a song, and that there is at least one y_2 for which if y_2 listens to a song, then y_2 is sleeping we can infer that there is at least one y_2 for which y_2 will sleep if and only if y_2 will listen to a song. Finally, from the fact that there is at least one y_2 for which y_2 will sleep if and only if y_2 will listen to a song we can infer that there is at least one y_2 for which if y_2 sleeps, then y_2 is listening to a song. Therefore, the answer is yes.