Consider the following premises. For all x, if x listens to a song, then x is rich. For all x, if x were bored, then x is a nurse. There is at least one x for which if x were rich, then x is bored. For all x, x will listen to a song if and only if x is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which if x were rich, then x is bored.
That is one of the premises. Therefore, the answer is yes.