Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  so0 Structured version   Unicode version

Theorem so0 4537
 Description: Any relation is a strict ordering of the empty set. (Contributed by NM, 16-Mar-1997.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
so0

Proof of Theorem so0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 po0 4519 . 2
2 ral0 3733 . 2
3 df-so 4505 . 2
41, 2, 3mpbir2an 888 1
 Colors of variables: wff set class Syntax hints:   w3o 936  wral 2706  c0 3629   class class class wbr 4213   wpo 4502   wor 4503 This theorem is referenced by:  we0  4578 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-v 2959  df-dif 3324  df-nul 3630  df-po 4504  df-so 4505
 Copyright terms: Public domain W3C validator