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