Consider the following premises. There is at least one x_8 for which x_8 will write a letter if and only if x_8 will climb a mountain. For all x_8, if x_8 plays tennis, then x_8 is writing a letter. For all x_8, if x_8 climbs a mountain, then x_8 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, the fact that x_8 writes a letter does not imply that x_8 is climbing a mountain.
That contradicts the premises. Therefore the answer is no.