Consider the following premises. Barbara is a writer if and only if David is a politician. David is a politician if and only if Jennifer is playing tennis. If Barbara were a writer, then Jennifer is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: The fact that Barbara were a writer does not imply that David is a politician.
 From the fact that David is a politician if and only if Jennifer is playing tennis we can infer that if Jennifer plays tennis, then David is a politician via biconditional elimination. From the fact that Barbara is a writer if and only if David is a politician we can infer that if David were a politician, then Barbara is a writer via biconditional elimination. Finally, from the fact that if Barbara were a writer, then Jennifer is playing tennis, and that if Jennifer plays tennis, then David is a politician we can infer that if Barbara were a writer, then David is a politician via transitivity, which contradicts that The fact that Barbara were a writer does not imply that David is a politician. Therefore, the answer is no.