Consider the following premises. If David plays a game, then it is late. It is cloudy if and only if it is late. David is playing a game. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that David is playing a game we can infer that David is playing a game or it is cloudy via addition. From the fact that it is cloudy if and only if it is late we can infer that if it is cloudy, then it is late via biconditional elimination. Finally, from the fact that if David plays a game, then it is late, that if it is cloudy, then it is late, and that David is playing a game or it is cloudy we can infer that it is late via disjunction elimination. Therefore, the answer is yes.