Corollary

If $(E_\iota)_{\iota \in I}$ is any family of sets, the cardinal of the union $\bigcup_{\iota \in I} E_\iota$ is at most equal to the sum $\sum_{\iota \in I}$ Card $(E_\iota)$.

For there exists a mapping of the sum S of the $\mathrm{E}_\iota$ onto the union of the $\mathrm{E}_\iota$ (Chapter II, § 4, no. 8); the Corollary therefore follows from Propositions 3 and 4.