Consider the following premises. For all y, y will play a game if and only if y will climb a mountain. There is at least one y for which y will climb a mountain if and only if y will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all y, the fact that y plays tennis does not imply that y is playing a game.
That contradicts the premises. Therefore the answer is no.