Consider the following premises. Barbara is listening to a song if and only if it is late. Elisabeth is poor. Barbara is listening to a song if and only if Elisabeth is poor. Can we infer the following from them? If we can, name the inference rule being used: Barbara is listening to a song.
 From the fact that Elisabeth is poor we can infer that Elisabeth is poor or it is late via addition. From the fact that Barbara is listening to a song if and only if Elisabeth is poor we can infer that if Elisabeth were poor, then Barbara is listening to a song via biconditional elimination. From the fact that Barbara is listening to a song if and only if it is late we can infer that if it is late, then Barbara is listening to a song via biconditional elimination. Finally, from the fact that if Elisabeth were poor, then Barbara is listening to a song, that if it is late, then Barbara is listening to a song, and that Elisabeth is poor or it is late we can infer that Barbara is listening to a song via disjunction elimination. Therefore, the answer is yes.