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Theorem opabid 4179
 Description: The law of concretion. Special case of Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
opabid

Proof of Theorem opabid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2689 . . 3
2 vex 2689 . . 3
31, 2opex 4151 . 2
4 copsexg 4166 . . 3
54bicomd 140 . 2
6 df-opab 3990 . 2
73, 5, 6elab2 2832 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wceq 1331  wex 1468   wcel 1480  cop 3530  copab 3988 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-opab 3990 This theorem is referenced by:  opelopabsb  4182  ssopab2b  4198  dmopab  4750  rnopab  4786  funopab  5158  funco  5163  fvmptss2  5496  f1ompt  5571  ovid  5887  enssdom  6656
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