Consider the following premises. For all x_2, if x_2 goes running, then x_2 is fast. There is at least one x_2 for which if x_2 were fast, then x_2 is cooking. For all x_2, x_2 will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which if x_2 were fast, then x_2 is cooking.
That is one of the premises. Therefore, the answer is yes.