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Theorem opelopabga 4731
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by Mario Carneiro, 19-Dec-2013.)
Hypothesis
Ref Expression
opelopabga.1
Assertion
Ref Expression
opelopabga
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem opelopabga
StepHypRef Expression
1 elopab 4726 . 2
2 opelopabga.1 . . 3
32copsex2g 4706 . 2
41, 3syl5bb 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   wceq 1438  wex 1660   wcel 1869  cop 4003  copab 4479 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pr 4658 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-rab 2785  df-v 3084  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-opab 4481 This theorem is referenced by:  brabga  4732  opelopab2a  4733  opelopaba  4734  opelopabg  4736  fmptsng  6098  isprmpt2  6977  canthwelem  9077  iswlk  25240  istrl  25259  ispth  25290  isspth  25291  isclwlk0  25474  isrngo  26098
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