Example 2

Tag 03S4, permanent. Cite it as [Bourbaki, Tag 03S4].

Theory of Sets, chapter II, § 3. Correspondences

Let G be a set of ordered pairs. The functions

z \to \mathrm{pr}_1 z \quad (z \in \mathrm{G}, \ \mathrm{pr}_1 z \in \mathrm{pr}_1 \mathrm{G})

and

z \to \mathrm{pr}_2 z \quad (z \in \mathrm{G}, \ \mathrm{pr}_2 z \in \mathrm{pr}_2 \mathrm{G})

are called respectively the first and second coordinate functions on G; they are denoted by $\mathrm{pr}_1$ and $\mathrm{pr}_2$ when there is no risk of confusion.

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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