Consider the following premises. Barbara is not a mechanic. For all y, y is a mechanic if and only if y will make tea. If Barbara makes tea, then Barbara is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Barbara is making tea.
 From the fact that for all y, y is a mechanic if and only if y will make tea we can infer that for all y, if y were a mechanic, then y is making tea via universal biconditional elimination. From the fact that for all y, if y were a mechanic, then y is making tea we can infer that if Barbara were a mechanic, then Barbara is making tea via universal instantiation. From the fact that if Barbara were a mechanic, then Barbara is making tea, and that if Barbara makes tea, then Barbara is a mechanic we can infer that Barbara is a mechanic if and only if Barbara is making tea via biconditional introduction. Finally, from the fact that Barbara is a mechanic if and only if Barbara is making tea, and that Barbara is not a mechanic we can infer that Barbara is not making tea via biconditional elimination, which contradicts that Barbara is making tea. Therefore, the answer is no.