Consider the following premises. There is at least one y for which if y listens to a song, then y is making tea. For all y, if y makes tea, then y is drinking water. For all y, 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: There is at least one y for which if y makes tea, then y is listening to a song.
 From the fact that for all y, if y makes tea, then y is drinking water, and that for all y, if y drinks water, then y is listening to a song we can infer that for all y, if y makes tea, then y is listening to a song via universal transitivity. From the fact that there is at least one y for which if y listens to a song, then y is making tea, and that for all y, if y makes tea, then y is listening to a song we can infer that there is at least one y for which y will listen to a song if and only if y will make tea via existential biconditional introduction. Finally, from the fact that there is at least one y for which y will listen to a song if and only if y will make tea we can infer that there is at least one y for which if y makes tea, then y is listening to a song via existential biconditional elimination. Therefore, the answer is yes.