Consider the following premises. It is cold. Mary is cooking if and only if Elisabeth is a bartender. If Mary cooks, then it is not cold. Can we infer the following from them? Elisabeth is not a bartender.
 From the fact that if Mary cooks, then it is not cold, and that it is cold we can infer that Mary is not cooking. Finally, from the fact that Mary is cooking if and only if Elisabeth is a bartender, and that Mary is not cooking we can infer that Elisabeth is not a bartender. Therefore, the answer is yes.