Consider the following premises. For all z, z will drive a car if and only if z will climb a mountain. For all z, z will drive a car if and only if z will write a letter. Can we infer the following from them? For all z, if z writes a letter, then z is climbing a mountain.
 From the fact that for all z, z will drive a car if and only if z will climb a mountain we can infer that for all z, if z drives a car, then z is climbing a mountain. From the fact that for all z, z will drive a car if and only if z will write a letter we can infer that for all z, if z writes a letter, then z is driving a car. Finally, from the fact that for all z, if z writes a letter, then z is driving a car, and that for all z, if z drives a car, then z is climbing a mountain we can infer that for all z, if z writes a letter, then z is climbing a mountain. Therefore, the answer is yes.