Consider the following premises. For all y, y will write a letter or y is not rich. There is at least one y for which y is rich if and only if y will listen to a song. Can we infer the following from them? There is at least one y for which if y listens to a song, then y is writing a letter.
 From the fact that there is at least one y for which y is rich if and only if y will listen to a song we can infer that there is at least one y for which if y listens to a song, then y is rich. From the fact that for all y, y will write a letter or y is not rich we can infer that for all y, if y were rich, then y is writing a letter. Finally, from the fact that there is at least one y for which if y listens to a song, then y is rich, and that for all y, if y were rich, then y is writing a letter we can infer that there is at least one y for which if y listens to a song, then y is writing a letter. Therefore, the answer is yes.