Consider the following premises. Patricia is not a soldier. Patricia is a soldier or Karen is not sleeping. If Patricia were a soldier, then Karen is sleeping. Can we infer the following from them? If we can, name the inference rule being used: Karen is not sleeping.
 From the fact that Patricia is a soldier or Karen is not sleeping we can infer that if Karen sleeps, then Patricia is a soldier via rewriting. From the fact that if Karen sleeps, then Patricia is a soldier, and that if Patricia were a soldier, then Karen is sleeping we can infer that Karen is sleeping if and only if Patricia is a soldier via biconditional introduction. Finally, from the fact that Karen is sleeping if and only if Patricia is a soldier, and that Patricia is not a soldier we can infer that Karen is not sleeping via biconditional elimination. Therefore, the answer is yes.