Consider the following premises. For all x_3, x_3 will play a game if and only if x_3 will climb a mountain. There is at least one x_3 for which if x_3 drives a car, then x_3 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, the fact that x_3 drives a car does not imply that x_3 is climbing a mountain.
That contradicts the premises. Therefore the answer is no.