Consider the following premises. If Michael were an astronaut, then it is cold. If Robert were fast, then Michael is an astronaut. Robert is fast or it is not cold. Can we infer the following from them? If we can, name the inference rule being used: If it is cold, then Robert is fast.
 From the fact that if Robert were fast, then Michael is an astronaut, and that if Michael were an astronaut, then it is cold we can infer that if Robert were fast, then it is cold via transitivity. Finally, from the fact that Robert is fast or it is not cold we can infer that if it is cold, then Robert is fast via rewriting. Therefore, the answer is yes.