Consider the following premises. There is at least one y_2 for which if y_2 writes a letter, then y_2 is poor. For all y_2, y_2 is fast. For all y_2, if y_2 writes a letter, then y_2 is not fast. For all y_2, if y_2 were poor, then y_2 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all y_2, if y_2 writes a letter, then y_2 is not fast.
That is one of the premises. Therefore, the answer is yes.