Theorem ordfr 6174

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

Step	Hyp	Ref	Expression
1		ordwe 6172	. 2 ⊢ (Ord 𝐴 → E We 𝐴)
2		wefr 5509	. 2 ⊢ ( E We 𝐴 → E Fr 𝐴)
3	1, 2	syl 17	1 ⊢ (Ord 𝐴 → E Fr 𝐴)

Syntax hints:   → wi 4   E cep 5429   Fr wfr 5475   We wwe 5477  Ord word 6158

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 5480  df-ord 6162

This theorem is referenced by:  ordirr  6177  tz7.7  6185  onfr  6198  bnj580  32295  bnj1053  32358  bnj1071  32359