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Theorem opelopabga 4185
 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 4180 . 2
2 opelopabga.1 . . 3
32copsex2g 4168 . 2
41, 3syl5bb 191 1
 Colors of variables: wff set class Syntax hints:   wi 4   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:  brabga  4186  opelopab2a  4187  opelopaba  4188  opelopabg  4190  rbropapd  6139  hashennn  10533
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