Consider the following premises. For all x, if x listens to a song, then x is playing tennis. For all x, if x plays tennis, then x is listening to a song. There is at least one x for which x will play tennis if and only if x will listen to a song. Can we infer the following from them? There is at least one x for which x will listen to a song if and only if x will play tennis.
 From the fact that for all x, if x listens to a song, then x is playing tennis, and that for all x, if x plays tennis, then x is listening to a song we can infer that for all x, x will listen to a song if and only if x will play tennis. From the fact that there is at least one x for which x will play tennis if and only if x will listen to a song we can infer that there is at least one x for which if x listens to a song, then x is playing tennis. From the fact that for all x, x will listen to a song if and only if x will play tennis we can infer that for all x, if x plays tennis, then x is listening to a song. Finally, from the fact that there is at least one x for which if x listens to a song, then x is playing tennis, and that for all x, if x plays tennis, then x is listening to a song we can infer that there is at least one x for which x will listen to a song if and only if x will play tennis. Therefore, the answer is yes.