Consider the following premises. For all x_5, x_5 will write a letter if and only if x_5 will play squash. For all x_5, if x_5 sleeps, then x_5 is writing a letter. There is at least one x_5 for which x_5 will play squash. Can we infer the following from them? For all x_5, if x_5 sleeps, then x_5 is writing a letter.
That is one of the premises. Therefore, the answer is yes.