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Theorem opelopabsbOLD 4464
 Description: The law of concretion in terms of substitutions. (Contributed by NM, 30-Sep-2002.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
opelopabsbOLD
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,,)

Proof of Theorem opelopabsbOLD
StepHypRef Expression
1 excom 1757 . . 3
2 vex 2960 . . . . . . 7
3 vex 2960 . . . . . . 7
42, 3opth 4436 . . . . . 6
5 equcom 1693 . . . . . . 7
6 equcom 1693 . . . . . . 7
75, 6anbi12ci 681 . . . . . 6
84, 7bitri 242 . . . . 5
98anbi1i 678 . . . 4
1092exbii 1594 . . 3
111, 10bitri 242 . 2
12 elopab 4463 . 2
13 2sb5 2189 . 2
1411, 12, 133bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wceq 1653  wsb 1659   wcel 1726  cop 3818  copab 4266 This theorem is referenced by:  brabsbOLD  4465  inopab  5006  cnvopab  5275  brabsb2  26712 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-opab 4268
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