Theorem ordfr 6377

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 6375	. 2 ⊢ (Ord 𝐴 → E We 𝐴)
2		wefr 5640	. 2 ⊢ ( E We 𝐴 → E Fr 𝐴)
3	1, 2	syl 18	1 ⊢ (Ord 𝐴 → E Fr 𝐴)

This proof depends on syntax axioms:   → wi 4   E cep 5549   Fr wfr 5600   We wwe 5602  Ord word 6361

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-we 5605  df-ord 6365

This theorem is used by:  ordirr  6380  tz7.7  6388  onfr  6402  bnj580  35543  bnj1053  35606  bnj1071  35607