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