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Theorem wefr 4152
Description: A well-ordering is well-founded. (Contributed by NM, 22-Apr-1994.)
Assertion
Ref Expression
wefr  |-  ( R  We  A  ->  R  Fr  A )

Proof of Theorem wefr
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-wetr 4128 . 2  |-  ( R  We  A  <->  ( R  Fr  A  /\  A. x  e.  A  A. y  e.  A  A. z  e.  A  ( (
x R y  /\  y R z )  ->  x R z ) ) )
21simplbi 268 1  |-  ( R  We  A  ->  R  Fr  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wral 2355   class class class wbr 3814    Fr wfr 4122    We wwe 4124
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-wetr 4128
This theorem is referenced by:  wepo  4153  wetriext  4358
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