Consider the following premises. If Barbara were a mechanic, then it is snowing. For all x_10, if x_10 works, then x_10 is a mechanic. If it snows, then Barbara is working. Can we infer the following from them? Barbara is working if and only if it is snowing.
 From the fact that for all x_10, if x_10 works, then x_10 is a mechanic we can infer that if Barbara works, then Barbara is a mechanic. From the fact that if Barbara works, then Barbara is a mechanic, and that if Barbara were a mechanic, then it is snowing we can infer that if Barbara works, then it is snowing. Finally, from the fact that if Barbara works, then it is snowing, and that if it snows, then Barbara is working we can infer that Barbara is working if and only if it is snowing. Therefore, the answer is yes.