Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eltp Unicode version

Theorem eltp 3678
 Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of [TakeutiZaring] p. 17. (Contributed by NM, 8-Apr-1994.) (Revised by Mario Carneiro, 11-Feb-2015.)
Hypothesis
Ref Expression
eltp.1
Assertion
Ref Expression
eltp

Proof of Theorem eltp
StepHypRef Expression
1 eltp.1 . 2
2 eltpg 3676 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wb 176   w3o 933   wceq 1623   wcel 1684  cvv 2788  ctp 3642 This theorem is referenced by:  dftp2  3679  tpid1  3739  tpid2  3740  tpid3  3742  brtp  24106  sltsolem1  24322  bpoly3  24793  fnckle  26045  frgra3vlem1  28178  frgra3vlem2  28179 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647  df-tp 3648
 Copyright terms: Public domain W3C validator