Consider the following premises. It is cold if and only if Barbara is working. It is cold if and only if Mary is an office clerk. Barbara is an astronaut. Barbara is not working. Can we infer the following from them? If we can, name the inference rule being used: Barbara is an astronaut and Mary is not an office clerk.
 From the fact that it is cold if and only if Barbara is working, and that Barbara is not working we can infer that it is not cold via biconditional elimination. From the fact that it is cold if and only if Mary is an office clerk, and that it is not cold we can infer that Mary is not an office clerk via biconditional elimination. Finally, from the fact that Barbara is an astronaut, and that Mary is not an office clerk we can infer that Barbara is an astronaut and Mary is not an office clerk via conjunction. Therefore, the answer is yes.