Consider the following premises. William is happy if and only if Sarah is a politician. Sarah is a politician if and only if William is happy. Can we infer the following from them? If we can, name the inference rule being used: If William were happy, then Sarah is a politician.
 From the fact that Sarah is a politician if and only if William is happy we can infer that if Sarah were a politician, then William is happy via biconditional elimination. Finally, from the fact that William is happy if and only if Sarah is a politician we can infer that if William were happy, then Sarah is a politician via biconditional elimination. Therefore, the answer is yes.