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Theorem opelopabsbALT 4761
Description: The law of concretion in terms of substitutions. Less general than opelopabsb 4762, but having a much shorter proof. (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
opelopabsbALT
Distinct variable groups:   , ,   , ,

Proof of Theorem opelopabsbALT
StepHypRef Expression
1 excom 1849 . . 3
2 vex 3112 . . . . . . 7
3 vex 3112 . . . . . . 7
42, 3opth 4726 . . . . . 6
5 equcom 1794 . . . . . . 7
6 equcom 1794 . . . . . . 7
75, 6anbi12ci 698 . . . . . 6
84, 7bitri 249 . . . . 5
98anbi1i 695 . . . 4
1092exbii 1668 . . 3
111, 10bitri 249 . 2
12 elopab 4760 . 2
13 2sb5 2187 . 2
1411, 12, 133bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  <.cop 4035  {copab 4509
This theorem is referenced by:  inopab  5138  cnvopab  5412  brabsb2  30603
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-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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