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Theorem abid2 2261
 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 170 . . 3 (𝑥𝐴𝑥𝐴)
21abbi2i 2255 . 2 𝐴 = {𝑥𝑥𝐴}
32eqcomi 2144 1 {𝑥𝑥𝐴} = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1332   ∈ wcel 1481  {cab 2126 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136 This theorem is referenced by:  csbid  3016  abss  3172  ssab  3173  abssi  3178  notab  3352  inrab2  3355  dfrab2  3357  dfrab3  3358  notrab  3359  eusn  3606  dfopg  3712  iunid  3877  csbexga  4065  imai  4904  dffv4g  5427  frec0g  6303  dfixp  6603  euen1b  6706  acfun  7083  ccfunen  7116
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