Consider the following premises. It is cold or Robert is not writing a letter. Robert is not writing a letter. If it is cold, then Robert is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that it is cold or Robert is not writing a letter we can infer that if Robert writes a letter, then it is cold via rewriting. From the fact that if Robert writes a letter, then it is cold, and that if it is cold, then Robert is writing a letter we can infer that Robert is writing a letter if and only if it is cold via biconditional introduction. Finally, from the fact that Robert is writing a letter if and only if it is cold, and that Robert is not writing a letter we can infer that it is not cold via biconditional elimination, which contradicts that It is cold. Therefore, the answer is no.