Consider the following premises. For all x, x will take a plane if and only if x is a writer. If Richard takes a plane, then Susan is bored. Susan is bored if and only if Richard is a writer. Can we infer the following from them? If we can, name the inference rule being used: Richard is a writer if and only if Susan is bored.
 From the fact that for all x, x will take a plane if and only if x is a writer we can infer that for all x, if x were a writer, then x is taking a plane via universal biconditional elimination. From the fact that for all x, if x were a writer, then x is taking a plane we can infer that if Richard were a writer, then Richard is taking a plane via universal instantiation. From the fact that if Richard were a writer, then Richard is taking a plane, and that if Richard takes a plane, then Susan is bored we can infer that if Richard were a writer, then Susan is bored via transitivity. From the fact that Susan is bored if and only if Richard is a writer we can infer that if Susan were bored, then Richard is a writer via biconditional elimination. Finally, from the fact that if Richard were a writer, then Susan is bored, and that if Susan were bored, then Richard is a writer we can infer that Richard is a writer if and only if Susan is bored via biconditional introduction. Therefore, the answer is yes.