Consider the following premises. For all x_9, if x_9 were fast, then x_9 is writing a letter. For all x_9, if x_9 writes a letter, then x_9 is fast. For all x_9, if x_9 writes a letter, then x_9 is happy. For all x_9, if x_9 cooks, then x_9 is writing a letter. For all x_9, x_9 will cook or x_9 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, if x_9 writes a letter, then x_9 is fast.
That is one of the premises. Therefore, the answer is yes.