Consider the following premises. For all x_12, x_12 will not listen to a song. For all x_12, x_12 will listen to a song if and only if x_12 is poor. For all x_12, if x_12 were rich, then x_12 is bored. For all x_12, x_12 is rich if and only if x_12 is bored. For all x_12, x_12 is rich if and only if x_12 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 will listen to a song if and only if x_12 is poor.
That is one of the premises. Therefore, the answer is yes.