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Theorem opelopaba 4281
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
opelopaba.1
opelopaba.2
opelopaba.3
Assertion
Ref Expression
opelopaba
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem opelopaba
StepHypRef Expression
1 opelopaba.1 . 2
2 opelopaba.2 . 2
3 opelopaba.3 . . 3
43opelopabga 4278 . 2
51, 2, 4mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1623   wcel 1684  cvv 2788  cop 3643  copab 4076 This theorem is referenced by:  canthwelem  8272  canthwe  8273  bcthlem1  18746 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078
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