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

Step	Hyp	Ref	Expression
1		ordwe 5952	. 2 ⊢ (Ord 𝐴 → E We 𝐴)
2		wefr 5300	. 2 ⊢ ( E We 𝐴 → E Fr 𝐴)
3	1, 2	syl 17	1 ⊢ (Ord 𝐴 → E Fr 𝐴)

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