New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  eltpg Unicode version

Theorem eltpg 3769
 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 3750 . . 3
2 elsncg 3755 . . 3
31, 2orbi12d 690 . 2
4 df-tp 3743 . . . 4
54eleq2i 2417 . . 3
6 elun 3220 . . 3
75, 6bitri 240 . 2
8 df-3or 935 . 2
93, 7, 83bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wo 357   w3o 933   wceq 1642   wcel 1710   cun 3207  csn 3737  cpr 3738  ctp 3739 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-tp 3743 This theorem is referenced by:  eltpi  3770  eltp  3771
 Copyright terms: Public domain W3C validator