Example 5

Tag 03T1, permanent. Cite it as [Bourbaki, Tag 03T1].

Theory of Sets, chapter III, § 2. Well-ordered sets

Let E be a well-ordered set. The set $\mathrm{E}_1$ obtained by adjoining to E a greatest element $b$ (§ 1, no. 7) is well-ordered, for if H is any non-empty subset of $\mathrm{E}_1$ other than $\{b\}$ , the least element of $\mathrm{H} \cap \mathrm{E}$ is also the least element of H.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

§ 1, no. 7