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