Consider the following premises. If it is windy, then it is sunny. Thomas is happy and it is cloudy. Thomas is happy if and only if it is windy. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that Thomas is happy if and only if it is windy we can infer that if Thomas were happy, then it is windy via biconditional elimination. From the fact that if Thomas were happy, then it is windy, and that if it is windy, then it is sunny we can infer that if Thomas were happy, then it is sunny via transitivity. From the fact that Thomas is happy and it is cloudy we can infer that Thomas is happy via simplification. Finally, from the fact that if Thomas were happy, then it is sunny, and that Thomas is happy we can infer that it is sunny via modus ponens. Therefore, the answer is yes.