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Theorem sopo 4230
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 4214 . 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 272 1  |-  ( R  Or  A  ->  R  Po  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 697   A.wral 2414   class class class wbr 3924    Po wpo 4211    Or wor 4212
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-iso 4214
This theorem is referenced by:  sonr  4234  sotr  4235  so2nr  4238  so3nr  4239  sosng  4607  fimaxq  10566
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