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Theorem opabid 4759
 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 opex 4716 . 2
2 copsexg 4737 . . 3
32bicomd 201 . 2
4 df-opab 4511 . 2
51, 3, 4elab2 3249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  <.cop 4035  {copab 4509 This theorem is referenced by:  opelopabsb  4762  ssopab2b  4779  dmopab  5218  rnopab  5252  funopab  5626  opabiota  5936  fvopab5  5979  f1ompt  6053  ovid  6419  zfrep6  6768  enssdom  7560  omxpenlem  7638  infxpenlem  8412  canthwelem  9049  pospo  15603  2ndcdisj  19957  lgsquadlem1  23629  lgsquadlem2  23630  h2hlm  25897  opabdm  27464  opabrn  27465  fpwrelmap  27556  eulerpartlemgvv  28315  areaquad  31184  diclspsn  36921 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511
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