Consider the following premises. For all y_1, y_1 will listen to a song if and only if y_1 is sad. For all y_1, if y_1 cooks, then y_1 is listening to a song. There is at least one y_1 for which y_1 will cook or y_1 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 will listen to a song.
 From the fact that for all y_1, y_1 will listen to a song if and only if y_1 is sad we can infer that for all y_1, if y_1 were sad, then y_1 is listening to a song via universal biconditional elimination. Finally, from the fact that for all y_1, if y_1 cooks, then y_1 is listening to a song, that for all y_1, if y_1 were sad, then y_1 is listening to a song, and that there is at least one y_1 for which y_1 will cook or y_1 is sad we can infer that there is at least one y_1 for which y_1 will listen to a song via existential disjunction elimination. Therefore, the answer is yes.