Consider the following premises. For all x, if x plays a game, then x is playing tennis. John is playing tennis or John is not playing a game. For all x, if x plays tennis, then x is playing a game. Can we infer the following from them? If we can, name the inference rule being used: If is not true that John is playing a game if and only if John is playing tennis.
That contradicts the premises. Therefore the answer is no.