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Theorem opelopabg 4770
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 28-May-1995.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
opelopabg.1
opelopabg.2
Assertion
Ref Expression
opelopabg
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem opelopabg
StepHypRef Expression
1 opelopabg.1 . . 3
2 opelopabg.2 . . 3
31, 2sylan9bb 699 . 2
43opelopabga 4765 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  <.cop 4035  {copab 4509
This theorem is referenced by:  opelopab  4774  fvopab3g  5952  fvopab3ig  5953  ov  6422  ovg  6441  joindef  15634  meetdef  15648  eltopspOLD  19419  istpsOLD  19421  iscom2  25414  isdivrngo  25433  isvclem  25470  adj1  26852  adjeq  26854  linedegen  29793  opelopab3  30207  bj-finsumval0  34663  dihpN  37063
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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