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Theorem ordfr 6195
Description: Membership is well-founded on an ordinal class. In other words, an ordinal class is well-founded. (Contributed by NM, 22-Apr-1994.)
Assertion
Ref Expression
ordfr (Ord 𝐴 → E Fr 𝐴)

Proof of Theorem ordfr
StepHypRef Expression
1 ordwe 6193 . 2 (Ord 𝐴 → E We 𝐴)
2 wefr 5533 . 2 ( E We 𝐴 → E Fr 𝐴)
31, 2syl 17 1 (Ord 𝐴 → E Fr 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   E cep 5452   Fr wfr 5499   We wwe 5501  Ord word 6179
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400  df-we 5504  df-ord 6183
This theorem is referenced by:  ordirr  6198  tz7.7  6206  onfr  6219  bnj580  32270  bnj1053  32333  bnj1071  32334
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