Consider the following premises. For all x_3, if x_3 plays tennis, then x_3 is writing a letter. For all x_3, if x_3 writes a letter, then x_3 is climbing a mountain. There is at least one x_3 for which if x_3 climbs a mountain, then x_3 is playing tennis. 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 climbs a mountain does not imply that x_3 is writing a letter.
That contradicts the premises. Therefore the answer is no.