Theorem ordfr 5655

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 5653	. 2 ⊢ (Ord 𝐴 → E We 𝐴)
2		wefr 5028	. 2 ⊢ ( E We 𝐴 → E Fr 𝐴)
3	1, 2	syl 17	1 ⊢ (Ord 𝐴 → E Fr 𝐴)

Syntax hints:   → wi 4   E cep 4947   Fr wfr 4994   We wwe 4996  Ord word 5639

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 196  df-an 385  df-we 4999  df-ord 5643

This theorem is referenced by:  ordirr  5658  tz7.7  5666  onfr  5680  bnj580  30237  bnj1053  30298  bnj1071  30299