Consider the following premises. For all x_4, if x_4 were bored, then x_4 is listening to a song. For all x_4, x_4 is bored if and only if x_4 is a lawyer. For all x_4, if x_4 listens to a song, then x_4 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is bored if and only if x_4 is a lawyer.
That is one of the premises. Therefore, the answer is yes.