Theorem bj-elabtru

Description: This is as close as we can get to proving extensionality for "the" "universal" class without ax-ext . (Contributed by BJ, 24-Apr-2024) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-elabtru	|- ( A e. { x | T. } <-> A e. { y | T. } )

Proof

Step	Hyp	Ref	Expression
1		bj-denoteslem	|- ( E. z z = A <-> A e. { x | T. } )
2		bj-denoteslem	|- ( E. z z = A <-> A e. { y | T. } )
3	1 2	bitr3i	|- ( A e. { x | T. } <-> A e. { y | T. } )