Consider the following premises. If Mary were a nurse, then Jennifer is a writer. It is raining if and only if Mary is a nurse. If Jennifer were a writer, then Mary is a nurse. Can we infer the following from them? If we can, name the inference rule being used: The fact that Jennifer were a writer does not imply that it is raining.
 From the fact that if Mary were a nurse, then Jennifer is a writer, and that if Jennifer were a writer, then Mary is a nurse we can infer that Mary is a nurse if and only if Jennifer is a writer via biconditional introduction. From the fact that it is raining if and only if Mary is a nurse we can infer that if Mary were a nurse, then it is raining via biconditional elimination. From the fact that Mary is a nurse if and only if Jennifer is a writer we can infer that if Jennifer were a writer, then Mary is a nurse via biconditional elimination. Finally, from the fact that if Jennifer were a writer, then Mary is a nurse, and that if Mary were a nurse, then it is raining we can infer that if Jennifer were a writer, then it is raining via transitivity, which contradicts that The fact that Jennifer were a writer does not imply that it is raining. Therefore, the answer is no.