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Theorem eltpg 4071
Description: Members of an unordered triple of classes. (Contributed by FL, 2-Feb-2014.) (Proof shortened by Mario Carneiro, 11-Feb-2015.)
Assertion
Ref Expression
eltpg

Proof of Theorem eltpg
StepHypRef Expression
1 elprg 4045 . . 3
2 elsncg 4052 . . 3
31, 2orbi12d 709 . 2
4 df-tp 4034 . . . 4
54eleq2i 2535 . . 3
6 elun 3644 . . 3
75, 6bitri 249 . 2
8 df-3or 974 . 2
93, 7, 83bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  \/wo 368  \/w3o 972  =wceq 1395  e.wcel 1818  u.cun 3473  {csn 4029  {cpr 4031  {ctp 4033
This theorem is referenced by:  eldiftp  4072  eltpi  4073  eltp  4074  f1dom3fv3dif  6175  f1dom3el3dif  6176  1cubr  23173  nb3graprlem1  24451  estrreslem2  32644
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  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-v 3111  df-un 3480  df-sn 4030  df-pr 4032  df-tp 4034
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