Consider the following premises. Thomas is bored or Sarah is not rich. If Thomas were bored, then Sarah is rich. Sarah is not rich. If Thomas were a lawyer, then Thomas is bored. Can we infer the following from them? If we can, name the inference rule being used: Thomas is a lawyer.
 From the fact that Thomas is bored or Sarah is not rich we can infer that if Sarah were rich, then Thomas is bored via rewriting. From the fact that if Thomas were bored, then Sarah is rich, and that if Sarah were rich, then Thomas is bored we can infer that Thomas is bored if and only if Sarah is rich via biconditional introduction. From the fact that Thomas is bored if and only if Sarah is rich, and that Sarah is not rich we can infer that Thomas is not bored via biconditional elimination. Finally, from the fact that if Thomas were a lawyer, then Thomas is bored, and that Thomas is not bored we can infer that Thomas is not a lawyer via modus tollens, which contradicts that Thomas is a lawyer. Therefore, the answer is no.