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Theorem eltpg 3444
 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 3423 . . 3
2 elsng 3418 . . 3
31, 2orbi12d 717 . 2
4 df-tp 3411 . . . 4
54eleq2i 2120 . . 3
6 elun 3112 . . 3
75, 6bitri 177 . 2
8 df-3or 897 . 2
93, 7, 83bitr4g 216 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102   wo 639   w3o 895   wceq 1259   wcel 1409   cun 2943  csn 3403  cpr 3404  ctp 3405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3or 897  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-tp 3411 This theorem is referenced by:  eltpi  3445  eltp  3446
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