Theorem abid2f

Description: A simplification of class abstraction. Theorem 5.2 of Quine p. 35. (Contributed by NM, 5-Sep-2011) (Revised by Mario Carneiro, 7-Oct-2016) (Proof shortened by Wolf Lammen, 17-Nov-2019)

	Ref	Expression
Hypothesis	abid2f.1	|- F/_ x A
Assertion	abid2f	|- { x | x e. A } = A

Proof

Step	Hyp	Ref	Expression
1		abid2f.1	|- F/_ x A
2		nfab1	|- F/_ x { x | x e. A }
3	2 1	cleqf	|- ( { x | x e. A } = A <-> A. x ( x e. { x | x e. A } <-> x e. A ) )
4		abid	|- ( x e. { x | x e. A } <-> x e. A )
5	3 4	mpgbir	|- { x | x e. A } = A