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Mirrors > Home > ILE Home > Th. List > ordfr | GIF version |
Description: Epsilon is well-founded on an ordinal class. (Contributed by NM, 22-Apr-1994.) |
Ref | Expression |
---|---|
ordfr | ⊢ (Ord 𝐴 → E Fr 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfregfr 4483 | . 2 ⊢ E Fr 𝐴 | |
2 | 1 | a1i 9 | 1 ⊢ (Ord 𝐴 → E Fr 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 E cep 4204 Fr wfr 4245 Ord word 4279 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-setind 4447 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-eprel 4206 df-frfor 4248 df-frind 4249 |
This theorem is referenced by: ordwe 4485 |
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