Theorem abid2 2158

Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 26-Dec-1993.)

Assertion

Ref	Expression
abid2	|- { x | x e. A } = A

Distinct variable group:   x, A

Proof of Theorem abid2

Step	Hyp	Ref	Expression
1		biid 160	. . 3 |- ( x e. A <-> x e. A )
2	1	abbi2i 2152	. 2 |- A = { x | x e. A }
3	2	eqcomi 2044	1 |- { x | x e. A } = A

Syntax hints:   = wceq 1243   e. wcel 1393   {cab 2026

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036

This theorem is referenced by:  csbid  2859  abss  3009  ssab  3010  abssi  3015  notab  3207  inrab2  3210  dfrab2  3212  dfrab3  3213  notrab  3214  eusn  3444  dfopg  3547  iunid  3712  csbexga  3885  imai  4681  dffv4g  5175  frec0g  5983  euen1b  6283