E cannot be false in any world described by Dn, because if E were false in a world described by Dn, there would be two worlds exactly alike in all descriptive respects where E is true in one and false in the other

Now, although it is an odd sentence—a very long disjunction—there is an important fact about D: it entails E and it is entailed by E. If E is true, then one of the disjuncts of D must be true, because D contains a disjunct describing every world where E is true; hence, D will be true as well. On the other hand, if D is true, then one of its disjuncts must be true, say it is Dn. E could not be false in a world described by Dn because Dn is included as a disjunct of D. Hence, if E were false in a