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Theorem so0 4838
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 4820 . 2
2 ral0 3934 . 2
3 df-so 4806 . 2
41, 2, 3mpbir2an 920 1
Colors of variables: wff setvar class
Syntax hints:  \/w3o 972  A.wral 2807   c0 3784   class class class wbr 4452  Powpo 4803  Orwor 4804
This theorem is referenced by:  we0  4879  wemapso2  8000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785  df-po 4805  df-so 4806
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