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Theorem sopo 4076
Description: A strict linear order is a strict partial order. (Contributed by NM, 28-Mar-1997.)
Assertion
Ref Expression
sopo  |-  ( R  Or  A  ->  R  Po  A )

Proof of Theorem sopo
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-iso 4060 . 2  |-  ( R  Or  A  <->  ( R  Po  A  /\  A. x  e.  A  A. y  e.  A  A. z  e.  A  ( x R y  ->  (
x R z  \/  z R y ) ) ) )
21simplbi 268 1  |-  ( R  Or  A  ->  R  Po  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 662   A.wral 2349   class class class wbr 3793    Po wpo 4057    Or wor 4058
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-iso 4060
This theorem is referenced by:  sonr  4080  sotr  4081  so2nr  4084  so3nr  4085  sosng  4439
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