Consider the following premises. It is not sunny. For all x_7, x_7 will climb a mountain if and only if x_7 is a lawyer. Barbara is a lawyer if and only if it is sunny. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not climbing a mountain.
 From the fact that for all x_7, x_7 will climb a mountain if and only if x_7 is a lawyer we can infer that Barbara is climbing a mountain if and only if Barbara is a lawyer via universal instantiation. From the fact that Barbara is a lawyer if and only if it is sunny, and that it is not sunny we can infer that Barbara is not a lawyer via biconditional elimination. Finally, from the fact that Barbara is climbing a mountain if and only if Barbara is a lawyer, and that Barbara is not a lawyer we can infer that Barbara is not climbing a mountain via biconditional elimination. Therefore, the answer is yes.