Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  brtp Structured version   Unicode version

Theorem brtp 30396
 Description: A condition for a binary relation over an unordered triple. (Contributed by Scott Fenton, 8-Jun-2011.)
Hypotheses
Ref Expression
brtp.1
brtp.2
Assertion
Ref Expression
brtp

Proof of Theorem brtp
StepHypRef Expression
1 df-br 4424 . 2
2 opex 4685 . . 3
32eltp 4045 . 2
4 brtp.1 . . . 4
5 brtp.2 . . . 4
64, 5opth 4695 . . 3
74, 5opth 4695 . . 3
84, 5opth 4695 . . 3
96, 7, 83orbi123i 1195 . 2
101, 3, 93bitri 274 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   w3o 981   wceq 1437   wcel 1872  cvv 3080  ctp 4002  cop 4004   class class class wbr 4423 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pr 4660 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-tp 4003  df-op 4005  df-br 4424 This theorem is referenced by:  sltval2  30550  sltsgn1  30555  sltsgn2  30556  sltintdifex  30557  sltres  30558  sltsolem1  30562  nodenselem8  30582  nodense  30583  nobndup  30594  nobnddown  30595
 Copyright terms: Public domain W3C validator