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