Bourbaki

Example

Tag 077Q, permanent. Cite it as [Bourbaki, Tag 077Q].

Theory of Sets, chapter I, § 1. Terms and relations

In the theory of sets, in which ∈\in is a relational sign of weight 2, the following sequence of assemblies is a formative construction:

AA′A′′∈AA′∈AA′′¬∈AA′∨¬∈AA′∈AA′′τ∨¬∈□A′∈□A′′ \begin{array}{c} A\\ A'\\ A''\\ \in AA'\\ \in AA''\\ \neg\in AA'\\ \vee\neg\in AA'\in AA'' \\[2pt] \tau\vee\neg\in\square A'\in\square A'' \end{array}

Hence the assembly given as an example in no. 1 is a term in the theory of sets.*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

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Transcribed from the printed edition, 2004, Springer. Not translated.