Consider the following premises. Thomas is a lawyer or John is not an electrician. If Joseph were excited, then Thomas is a lawyer. John is an electrician. Can we infer the following from them? If we can, name the inference rule being used: Thomas is a lawyer.
 From the fact that John is an electrician we can infer that John is an electrician or Joseph is excited via addition. From the fact that Thomas is a lawyer or John is not an electrician we can infer that if John were an electrician, then Thomas is a lawyer via rewriting. Finally, from the fact that if John were an electrician, then Thomas is a lawyer, that if Joseph were excited, then Thomas is a lawyer, and that John is an electrician or Joseph is excited we can infer that Thomas is a lawyer via disjunction elimination. Therefore, the answer is yes.