Consider the following premises. Joseph is sleeping if and only if Michael is a soldier. If Joseph sleeps, then it is windy. If it is windy, then Michael is a soldier. Can we infer the following from them? If we can, name the inference rule being used: It is windy if and only if Joseph is sleeping.
 From the fact that Joseph is sleeping if and only if Michael is a soldier we can infer that if Michael were a soldier, then Joseph is sleeping via biconditional elimination. From the fact that if it is windy, then Michael is a soldier, and that if Michael were a soldier, then Joseph is sleeping we can infer that if it is windy, then Joseph is sleeping via transitivity. Finally, from the fact that if it is windy, then Joseph is sleeping, and that if Joseph sleeps, then it is windy we can infer that it is windy if and only if Joseph is sleeping via biconditional introduction. Therefore, the answer is yes.