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, 26-Feb-2025)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | abid2f.1 | |- F/_ x A |
|
| Assertion | abid2f | |- { x | x e. A } = A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | abid2f.1 | |- F/_ x A |
|
| 2 | 1 | eqabf | |- ( A = { x | x e. A } <-> A. x ( x e. A <-> x e. A ) ) |
| 3 | biid | |- ( x e. A <-> x e. A ) |
|
| 4 | 2 3 | mpgbir | |- A = { x | x e. A } |
| 5 | 4 | eqcomi | |- { x | x e. A } = A |