Theorem ordfr 5776

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 5774	. 2 ⊢ (Ord 𝐴 → E We 𝐴)
2		wefr 5133	. 2 ⊢ ( E We 𝐴 → E Fr 𝐴)
3	1, 2	syl 17	1 ⊢ (Ord 𝐴 → E Fr 𝐴)

Syntax hints:   → wi 4   E cep 5057   Fr wfr 5099   We wwe 5101  Ord word 5760

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 197  df-an 385  df-we 5104  df-ord 5764

This theorem is referenced by:  ordirr  5779  tz7.7  5787  onfr  5801  bnj580  31109  bnj1053  31170  bnj1071  31171