Consider the following premises. For all y, y will not drink water. For all y, if y listens to a song, then y is drinking water. There is at least one y for which if y drinks water, then y is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will listen to a song.
 From the fact that there is at least one y for which if y drinks water, then y is listening to a song, and that for all y, if y listens to a song, then y is drinking water we can infer that there is at least one y for which y will drink water if and only if y will listen to a song via existential biconditional introduction. Finally, from the fact that there is at least one y for which y will drink water if and only if y will listen to a song, and that for all y, y will not drink water we can infer that there is at least one y for which y will not listen to a song via existential biconditional elimination, which contradicts that For all y, y will listen to a song. Therefore, the answer is no.