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Theorem abid2 2174
Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 26-Dec-1993.)
Assertion
Ref Expression
abid2 {𝑥𝑥𝐴} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem abid2
StepHypRef Expression
1 biid 164 . . 3 (𝑥𝐴𝑥𝐴)
21abbi2i 2168 . 2 𝐴 = {𝑥𝑥𝐴}
32eqcomi 2060 1 {𝑥𝑥𝐴} = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wcel 1409  {cab 2042
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052
This theorem is referenced by:  csbid  2887  abss  3037  ssab  3038  abssi  3043  notab  3235  inrab2  3238  dfrab2  3240  dfrab3  3241  notrab  3242  eusn  3472  dfopg  3575  iunid  3740  csbexga  3913  imai  4709  dffv4g  5203  frec0g  6014  euen1b  6314
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