Consider the following premises. Elisabeth is not playing a game. If Elisabeth were a mechanic, then Elisabeth is playing a game. Elisabeth is a mechanic if and only if Elisabeth is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a mechanic.
 From the fact that Elisabeth is a mechanic if and only if Elisabeth is playing a game we can infer that if Elisabeth plays a game, then Elisabeth is a mechanic via biconditional elimination. From the fact that if Elisabeth plays a game, then Elisabeth is a mechanic, and that if Elisabeth were a mechanic, then Elisabeth is playing a game we can infer that Elisabeth is playing a game if and only if Elisabeth is a mechanic via biconditional introduction. Finally, from the fact that Elisabeth is playing a game if and only if Elisabeth is a mechanic, and that Elisabeth is not playing a game we can infer that Elisabeth is not a mechanic via biconditional elimination. Therefore, the answer is yes.