Consider the following premises. For all x_6, x_6 will climb a mountain if and only if x_6 will play a game. For all x_6, x_6 will play a game or x_6 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which the fact that x_6 writes a letter does not imply that x_6 is climbing a mountain.
 From the fact that for all x_6, x_6 will play a game or x_6 will not write a letter we can infer that for all x_6, if x_6 writes a letter, then x_6 is playing a game via universal rewriting. From the fact that for all x_6, x_6 will climb a mountain if and only if x_6 will play a game we can infer that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 writes a letter, then x_6 is playing a game, and that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 writes a letter, then x_6 is climbing a mountain via universal transitivity, which contradicts that There is at least one x_6 for which the fact that x_6 writes a letter does not imply that x_6 is climbing a mountain. Therefore, the answer is no.