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Theorem opelopabg 4176
 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 683 . 2
43opelopabga 4171 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360   wceq 1619   wcel 1621  cop 3547  copab 3973 This theorem is referenced by:  opelopab  4179  fvopab3g  5450  fvopab3ig  5451  ov  5819  ovg  5838  eltopspOLD  16488  istpsOLD  16490  iscom2  20909  isdivrngo  20928  isvclem  20963  adj1  22343  adjeq  22345  linedegen  23940  islatalg  24349  cmppar3  25140  opelopab3  25539  dihpN  30215 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-opab 3975
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