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| Description: Membership is well-founded on an ordinal class. In other words, an ordinal class is well-founded. (Contributed by NM, 22-Apr-1994.) | 
| Ref | Expression | 
|---|---|
| ordfr | ⊢ (Ord 𝐴 → E Fr 𝐴) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ordwe 6396 | . 2 ⊢ (Ord 𝐴 → E We 𝐴) | |
| 2 | wefr 5674 | . 2 ⊢ ( E We 𝐴 → E Fr 𝐴) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (Ord 𝐴 → E Fr 𝐴) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 E cep 5582 Fr wfr 5633 We wwe 5635 Ord word 6382 | 
| 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 207 df-an 396 df-we 5638 df-ord 6386 | 
| This theorem is referenced by: ordirr 6401 tz7.7 6409 onfr 6422 bnj580 34928 bnj1053 34991 bnj1071 34992 | 
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