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Theorem opelopabg 4719
 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:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem opelopabg
StepHypRef Expression
1 opelopabg.1 . . 3
2 opelopabg.2 . . 3
31, 2sylan9bb 714 . 2
43opelopabga 4714 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   wceq 1452   wcel 1904  cop 3965  copab 4453 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455 This theorem is referenced by:  opelopab  4723  fvopab3g  5959  fvopab3ig  5960  ov  6435  ovg  6454  joindef  16328  meetdef  16342  iscom2  26221  isdivrngo  26240  isvclem  26277  adj1  27667  adjeq  27669  linedegen  30981  bj-finsumval0  31772  opelopab3  32107  dihpN  34975
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