Consider the following premises. If it is overcast, then David is drinking water. If David drinks water, then James is playing tennis. It is overcast or David is playing a game. For all x_2, if x_2 plays a game, then x_2 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: James is playing tennis.
 From the fact that for all x_2, if x_2 plays a game, then x_2 is drinking water we can infer that if David plays a game, then David is drinking water via universal instantiation. From the fact that if it is overcast, then David is drinking water, that if David plays a game, then David is drinking water, and that it is overcast or David is playing a game we can infer that David is drinking water via disjunction elimination. Finally, from the fact that if David drinks water, then James is playing tennis, and that David is drinking water we can infer that James is playing tennis via modus ponens. Therefore, the answer is yes.