Consider the following premises. If Robert were a doctor, then Elisabeth is a politician. Richard is rich or Robert is a doctor. If Elisabeth were a politician, then it is cold. If Richard were rich, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if Robert were a doctor, then Elisabeth is a politician, and that if Elisabeth were a politician, then it is cold we can infer that if Robert were a doctor, then it is cold via transitivity. Finally, from the fact that if Richard were rich, then it is cold, that if Robert were a doctor, then it is cold, and that Richard is rich or Robert is a doctor we can infer that it is cold via disjunction elimination, which contradicts that It is not cold. Therefore, the answer is no.