Example 2

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

Theory of Sets, chapter III, § 1. Order relations. Ordered sets

In the set $\Phi(E, F)$ of mappings of subsets of E into F (F being non-empty), ordered by the relation " $v$ extends $u$ " between $u$ and $v$ , the maximal elements are the mappings of the whole of E into F.

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.

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