Consider the following premises. Michael is not a writer. If it is cold, then Michael is a writer. It is cold or Michael is not a writer. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that it is cold or Michael is not a writer we can infer that if Michael were a writer, then it is cold via rewriting. From the fact that if Michael were a writer, then it is cold, and that if it is cold, then Michael is a writer we can infer that Michael is a writer if and only if it is cold via biconditional introduction. Finally, from the fact that Michael is a writer if and only if it is cold, and that Michael is not a writer we can infer that it is not cold via biconditional elimination. Therefore, the answer is yes.