Consider the following premises. If James takes a plane, then it is cold. If Michael were happy, then it is cold. For all x_4, x_4 is happy. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that for all x_4, x_4 is happy we can infer that Michael is happy via universal instantiation. From the fact that Michael is happy we can infer that Michael is happy or James is taking a plane via addition. Finally, from the fact that if Michael were happy, then it is cold, that if James takes a plane, then it is cold, and that Michael is happy or James is taking a plane we can infer that it is cold via disjunction elimination. Therefore, the answer is yes.