Consider the following premises. For all x_6, x_6 is an office clerk or x_6 will not cook. For all x_6, if x_6 plays a game, then x_6 is cooking. For all x_6, if x_6 were an office clerk, then x_6 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if x_6 cooks, then x_6 is an office clerk.
 From the fact that for all x_6, if x_6 were an office clerk, then x_6 is playing a game, and that for all x_6, if x_6 plays a game, then x_6 is cooking we can infer that for all x_6, if x_6 were an office clerk, then x_6 is cooking via universal transitivity. Finally, from the fact that for all x_6, x_6 is an office clerk or x_6 will not cook we can infer that for all x_6, if x_6 cooks, then x_6 is an office clerk via universal rewriting. Therefore, the answer is yes.