Theorem 2

Tag 03P4, permanent. Cite it as [Bourbaki, Tag 03P4].

Theory of Sets, chapter I, § 5. Equalitarian theories

$(x = y) \Leftrightarrow (y = x)$ .

Suppose that the relation $x = y$ is true. By S6, the relation

(x = y) \Rightarrow ((x|y)(y = x) \Leftrightarrow (y|y)(y = x)),

that is

(x = y) \Rightarrow ((x = x) \Leftrightarrow (y = x)),

is true. Therefore $(x = x) \Leftrightarrow (y = x)$ is true. By Theorem 1 it follows that $y = x$ is true, and the theorem is proved.

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

Theorem 1