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Theorem eltpg 3853
 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 3833 . . 3
2 elsncg 3838 . . 3
31, 2orbi12d 692 . 2
4 df-tp 3824 . . . 4
54eleq2i 2502 . . 3
6 elun 3490 . . 3
75, 6bitri 242 . 2
8 df-3or 938 . 2
93, 7, 83bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wo 359   w3o 936   wceq 1653   wcel 1726   cun 3320  csn 3816  cpr 3817  ctp 3818 This theorem is referenced by:  eltpi  3854  eltp  3855  1cubr  20684  nb3graprlem1  21462  eldiftp  24395 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823  df-tp 3824
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