MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ordfr Structured version   Visualization version   GIF version

Theorem ordfr 5954
Description: Epsilon is well-founded on an ordinal class. (Contributed by NM, 22-Apr-1994.)
Assertion
Ref Expression
ordfr (Ord 𝐴 → E Fr 𝐴)

Proof of Theorem ordfr
StepHypRef Expression
1 ordwe 5952 . 2 (Ord 𝐴 → E We 𝐴)
2 wefr 5300 . 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 5222   Fr wfr 5266   We wwe 5268  Ord word 5938
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 199  df-an 386  df-we 5271  df-ord 5942
This theorem is referenced by:  ordirr  5957  tz7.7  5965  onfr  5978  bnj580  31492  bnj1053  31553  bnj1071  31554
  Copyright terms: Public domain W3C validator