Consider the following premises. It is sunny or James is not taking a plane. Michael is cooking or James is taking a plane. It is sunny if and only if Michael is cooking. 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 sunny or James is not taking a plane we can infer that if James takes a plane, then it is sunny via rewriting. From the fact that it is sunny if and only if Michael is cooking we can infer that if Michael cooks, then it is sunny via biconditional elimination. Finally, from the fact that if Michael cooks, then it is sunny, that if James takes a plane, then it is sunny, and that Michael is cooking or James is taking a plane we can infer that it is sunny via disjunction elimination. Therefore, the answer is yes.