Theorem eqabi

Description: Equality of a class variable and a class abstraction (inference form). (Contributed by NM, 26-May-1993) Avoid ax-11 . (Revised by Wolf Lammen, 6-May-2023)

	Ref	Expression
Hypothesis	eqabi.1	|- ( x e. A <-> ph )
Assertion	eqabi	|- A = { x | ph }

Proof

Step	Hyp	Ref	Expression
1		eqabi.1	|- ( x e. A <-> ph )
2	1	a1i	|- ( T. -> ( x e. A <-> ph ) )
3	2	eqabdv	|- ( T. -> A = { x | ph } )
4	3	mptru	|- A = { x | ph }