Consider the following premises. For all z_1, z_1 will play a game or z_1 will not climb a mountain. For all z_1, z_1 will climb a mountain or z_1 will not play a game. Can we infer the following from them? For all z_1, z_1 will climb a mountain or z_1 will not play a game.
That is one of the premises. Therefore, the answer is yes.