Description: Obsolete version of abid2f as of 26-Feb-2025. (Contributed by NM, 5-Sep-2011) (Revised by Mario Carneiro, 7-Oct-2016) (Proof shortened by Wolf Lammen, 17-Nov-2019) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | abid2f.1 | |- F/_ x A |
|
Assertion | abid2fOLD | |- { x | x e. A } = A |
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 |