Bourbaki

Example

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

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

The symbol τx(∈xy)\tau_x(\in xy) represents the assembly

τ∈□y. \tau\in\square y.

Let AA and BB be assemblies and let xx be a letter. The assembly obtained by replacing xx, wherever it occurs in AA, by the assembly BB is denoted by (B∣x) A(B\mathbin{|}x)\,A (read : BB replaces xx in AA). If xx does not appear in AA, then (B∣x) A(B\mathbin{|}x)\,A is identical with AA; in particular,

(B∣x) τx(A) (B\mathbin{|}x)\,\tau_x(A)

is identical with τx(A)\tau_x(A).

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

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Cites

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