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Theorem opelopab 4179
 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 4176 . 2
61, 2, 5mp2an 656 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wceq 1619   wcel 1621  cvv 2727  cop 3547  copab 3973 This theorem is referenced by:  opabid2  4722  dfres2  4909  f1oiso  5700  elopabi  6037  xporderlem  6078  cnlnssadj  22490  pellexlem3  26082  dicopelval  30056  dih1dimatlem  30208 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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