Consider the following premises. Richard is working if and only if it is late. Richard is working if and only if Thomas is a carpenter. Thomas is a carpenter or it is late. Can we infer the following from them? If we can, name the inference rule being used: Richard is working.
 From the fact that Richard is working if and only if Thomas is a carpenter we can infer that if Thomas were a carpenter, then Richard is working via biconditional elimination. From the fact that Richard is working if and only if it is late we can infer that if it is late, then Richard is working via biconditional elimination. Finally, from the fact that if Thomas were a carpenter, then Richard is working, that if it is late, then Richard is working, and that Thomas is a carpenter or it is late we can infer that Richard is working via disjunction elimination. Therefore, the answer is yes.