Consider the following premises. For all x_6, if x_6 were a musician, then x_6 is rich. For all x_6, if x_6 were excited, then x_6 is a musician. For all x_6, x_6 is not a politician. For all x_6, x_6 is a politician or x_6 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not a politician.
That is one of the premises. Therefore, the answer is yes.