Consider the following premises. For all y, if y were an electrician, then y is listening to a song. There is at least one y for which if y listens to a song, then y is excited. For all y, if y were excited, then y is an electrician. Can we infer the following from them? There is at least one y for which if y were excited, then y is an electrician.
 From the fact that for all y, if y were an electrician, then y is listening to a song, and that there is at least one y for which if y listens to a song, then y is excited we can infer that there is at least one y for which if y were an electrician, then y is excited. From the fact that for all y, if y were excited, then y is an electrician, and that there is at least one y for which if y were an electrician, then y is excited we can infer that there is at least one y for which y is excited if and only if y is an electrician. Finally, from the fact that there is at least one y for which y is excited if and only if y is an electrician we can infer that there is at least one y for which if y were excited, then y is an electrician. Therefore, the answer is yes.