Consider the following premises. There is at least one z_4 for which z_4 is a lawyer if and only if z_4 is a writer. For all z_4, z_4 is a writer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_4 for which z_4 is a lawyer or z_4 is rich.
 From the fact that there is at least one z_4 for which z_4 is a lawyer if and only if z_4 is a writer we can infer that there is at least one z_4 for which if z_4 were a writer, then z_4 is a lawyer via existential biconditional elimination. From the fact that there is at least one z_4 for which if z_4 were a writer, then z_4 is a lawyer, and that for all z_4, z_4 is a writer we can infer that there is at least one z_4 for which z_4 is a lawyer via existential modus ponens. Finally, from the fact that there is at least one z_4 for which z_4 is a lawyer we can infer that there is at least one z_4 for which z_4 is a lawyer or z_4 is rich via existential addition. Therefore, the answer is yes.