Consider the following premises. There is at least one x_13 for which x_13 will cook and x_13 is a sailor. For all x_13, if x_13 cooks, then x_13 is writing a letter. For all x_13, if x_13 climbs a mountain, then x_13 is writing a letter. For all x_13, if x_13 plays squash, then x_13 is climbing a mountain. Can we infer the following from them? For all x_13, if x_13 climbs a mountain, then x_13 is writing a letter.
That is one of the premises. Therefore, the answer is yes.