Consider the following premises. If Barbara were a mechanic, then it is sunny. It is sunny if and only if Barbara is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Barbara is a mechanic if and only if it is sunny.
 From the fact that it is sunny if and only if Barbara is a mechanic we can infer that if it is sunny, then Barbara is a mechanic via biconditional elimination. Finally, from the fact that if Barbara were a mechanic, then it is sunny, and that if it is sunny, then Barbara is a mechanic we can infer that Barbara is a mechanic if and only if it is sunny via biconditional introduction, which contradicts that If is not true that Barbara is a mechanic if and only if it is sunny. Therefore, the answer is no.