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Theorem eltpg 3689
 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 3670 . . 3
2 elsncg 3675 . . 3
31, 2orbi12d 690 . 2
4 df-tp 3661 . . . 4
54eleq2i 2360 . . 3
6 elun 3329 . . 3
75, 6bitri 240 . 2
8 df-3or 935 . 2
93, 7, 83bitr4g 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wo 357   w3o 933   wceq 1632   wcel 1696   cun 3163  csn 3653  cpr 3654  ctp 3655 This theorem is referenced by:  eltpi  3690  eltp  3691  1cubr  20154  eldiftp  23410  inttpemp  25242  pfsubkl  26150  usgraex0elv  28262  usgraex1elv  28263  usgraex2elv  28264  nb3graprlem1  28287 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660  df-tp 3661
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