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