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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  |-  { x  |  x  e.  A }  =  A
Distinct variable group:    x, A

Proof of Theorem abid2
StepHypRef Expression
1 biid 171 . . 3  |-  ( x  e.  A  <->  x  e.  A )
21abbi2i 2304 . 2  |-  A  =  { x  |  x  e.  A }
32eqcomi 2193 1  |-  { x  |  x  e.  A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1364    e. 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  3084  abss  3244  ssab  3245  abssi  3250  notab  3425  inrab2  3428  dfrab2  3430  dfrab3  3431  notrab  3432  eusn  3688  dfopg  3798  iunid  3964  csbexga  4153  imai  5009  dffv4g  5539  frec0g  6437  dfixp  6741  euen1b  6844  acfun  7253  ccfunen  7310
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