Consider the following premises. If it rains, then it is overcast. If it is overcast, then it is sunny. It is cold or it is not sunny. Can we infer the following from them? If we can, name the inference rule being used: If it rains, then it is cold.
 From the fact that if it rains, then it is overcast, and that if it is overcast, then it is sunny we can infer that if it rains, then it is sunny via transitivity. From the fact that it is cold or it is not sunny we can infer that if it is sunny, then it is cold via rewriting. Finally, from the fact that if it rains, then it is sunny, and that if it is sunny, then it is cold we can infer that if it rains, then it is cold via transitivity. Therefore, the answer is yes.