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Theorem abid2 2742
Description: A simplification of class abstraction. Commuted form of abid1 2741. See comments there. (Contributed by NM, 26-Dec-1993.)
Assertion
Ref Expression
abid2 {𝑥𝑥𝐴} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem abid2
StepHypRef Expression
1 abid1 2741 . 2 𝐴 = {𝑥𝑥𝐴}
21eqcomi 2630 1 {𝑥𝑥𝐴} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wcel 1987  {cab 2607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617
This theorem is referenced by:  csbid  3522  abss  3650  ssab  3651  abssi  3656  notab  3873  dfrab3  3878  notrab  3880  eusn  4235  uniintsn  4479  iunid  4541  csbexg  4752  imai  5437  dffv4  6145  orduniss2  6980  dfixp  7854  euen1b  7971  modom2  8106  infmap2  8984  cshwsexa  13507  ustfn  21915  ustn0  21934  fpwrelmap  29351  eulerpartlemgvv  30219  ballotlem2  30331  dffv5  31673  ptrest  33040  cnambfre  33090  pmapglb  34536  polval2N  34672  rngunsnply  37224  iocinico  37278
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