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