Consider the following premises. For all x_10, if x_10 plays a game, then x_10 is rich. For all x_10, if x_10 were poor, then x_10 is playing a game. For all x_10, if x_10 were rich, then x_10 is playing a game. For all x_10, x_10 is rich or x_10 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is rich or x_10 is poor.
That is one of the premises. Therefore, the answer is yes.