Consider the following premises. There is at least one x_3 for which if x_3 climbs a mountain, then x_3 is not playing a game. For all x_3, x_3 will play a game. For all x_3, x_3 will take a plane if and only if x_3 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will take a plane.
 From the fact that there is at least one x_3 for which if x_3 climbs a mountain, then x_3 is not playing a game, and that for all x_3, x_3 will play a game we can infer that there is at least one x_3 for which x_3 will not climb a mountain via existential modus tollens. Finally, from the fact that for all x_3, x_3 will take a plane if and only if x_3 will climb a mountain, and that there is at least one x_3 for which x_3 will not climb a mountain we can infer that there is at least one x_3 for which x_3 will not take a plane via existential biconditional elimination, which contradicts that For all x_3, x_3 will take a plane. Therefore, the answer is no.