Consider the following premises. For all x, x is a police officer if and only if x is happy. Barbara is a police officer if and only if Barbara is happy. Barbara is not happy. Can we infer the following from them? Barbara is not a police officer.
 From the fact that for all x, x is a police officer if and only if x is happy we can infer that Barbara is a police officer if and only if Barbara is happy. From the fact that Barbara is a police officer if and only if Barbara is happy we can infer that if Barbara were a police officer, then Barbara is happy. From the fact that Barbara is a police officer if and only if Barbara is happy we can infer that if Barbara were happy, then Barbara is a police officer. From the fact that if Barbara were happy, then Barbara is a police officer, and that if Barbara were a police officer, then Barbara is happy we can infer that Barbara is happy if and only if Barbara is a police officer. Finally, from the fact that Barbara is happy if and only if Barbara is a police officer, and that Barbara is not happy we can infer that Barbara is not a police officer. Therefore, the answer is yes.