Consider the following premises. If Robert works, then Patricia is cooking. If Robert works, then Elisabeth is a soldier. If Elisabeth were a soldier, then Robert is working. Patricia is not cooking. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a soldier.
 From the fact that if Robert works, then Patricia is cooking, and that Patricia is not cooking we can infer that Robert is not working via modus tollens. From the fact that if Robert works, then Elisabeth is a soldier, and that if Elisabeth were a soldier, then Robert is working we can infer that Robert is working if and only if Elisabeth is a soldier via biconditional introduction. Finally, from the fact that Robert is working if and only if Elisabeth is a soldier, and that Robert is not working we can infer that Elisabeth is not a soldier via biconditional elimination. Therefore, the answer is yes.