Consider the following premises. There is at least one x_7 for which if x_7 were sad, then x_7 is climbing a mountain. For all x_7, if x_7 climbs a mountain, then x_7 is writing a letter. For all x_7, x_7 is sad or x_7 will not cook. Can we infer the following from them? There is at least one x_7 for which if x_7 were sad, then x_7 is climbing a mountain.
That is one of the premises. Therefore, the answer is yes.