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Theorem abid2 2310
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 171 . . 3 (𝑥𝐴𝑥𝐴)
21abbi2i 2304 . 2 𝐴 = {𝑥𝑥𝐴}
32eqcomi 2193 1 {𝑥𝑥𝐴} = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1364  wcel 2160  {cab 2175
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185
This theorem is referenced by:  csbid  3080  abss  3239  ssab  3240  abssi  3245  notab  3420  inrab2  3423  dfrab2  3425  dfrab3  3426  notrab  3427  eusn  3681  dfopg  3791  iunid  3957  csbexga  4146  imai  5002  dffv4g  5531  frec0g  6423  dfixp  6727  euen1b  6830  acfun  7237  ccfunen  7294
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