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Theorem so0 4807
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  |-  R  Or  (/)

Proof of Theorem so0
Dummy variables  x  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 po0 4789 . 2  |-  R  Po  (/)
2 ral0 3904 . 2  |-  A. x  e.  (/)  A. y  e.  (/)  ( x R y  \/  x  =  y  \/  y R x )
3 df-so 4775 . 2  |-  ( R  Or  (/)  <->  ( R  Po  (/) 
/\  A. x  e.  (/)  A. y  e.  (/)  ( x R y  \/  x  =  y  \/  y R x ) ) )
41, 2, 3mpbir2an 928 1  |-  R  Or  (/)
Colors of variables: wff setvar class
Syntax hints:    \/ w3o 981   A.wral 2771   (/)c0 3761   class class class wbr 4423    Po wpo 4772    Or wor 4773
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-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-an 372  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-ral 2776  df-v 3082  df-dif 3439  df-nul 3762  df-po 4774  df-so 4775
This theorem is referenced by:  we0  4848  wemapso2  8077
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