Consider the following premises. For all x, if x were an artist, then x is listening to a song. For all x, if x were a doctor, then x is an artist. For all x, x is a doctor if and only if x will listen to a song. Can we infer the following from them? For all x, x is a doctor if and only if x will listen to a song.
That is one of the premises. Therefore, the answer is yes.