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Theorem opelopab 4008
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 16-May-1995.)
Hypotheses
Ref Expression
opelopab.1
opelopab.2
opelopab.3
opelopab.4
Assertion
Ref Expression
opelopab
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem opelopab
StepHypRef Expression
1 opelopab.1 . 2
2 opelopab.2 . 2
3 opelopab.3 . . 3
4 opelopab.4 . . 3
53, 4opelopabg 4005 . 2
61, 2, 5mp2an 402 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  cvv 2557  cop 3378  copab 3817 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819 This theorem is referenced by:  opabid2  4467  dfres2  4658  xporderlem  5852
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