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