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Mirrors > Home > ILE Home > Th. List > nordeq | Unicode version |
Description: A member of an ordinal class is not equal to it. (Contributed by NM, 25-May-1998.) |
Ref | Expression |
---|---|
nordeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordirr 4502 | . . . 4 | |
2 | eleq1 2220 | . . . . 5 | |
3 | 2 | notbid 657 | . . . 4 |
4 | 1, 3 | syl5ibcom 154 | . . 3 |
5 | 4 | necon2ad 2384 | . 2 |
6 | 5 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1335 wcel 2128 wne 2327 word 4323 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-setind 4497 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-v 2714 df-dif 3104 df-sn 3566 |
This theorem is referenced by: phplem1 6798 |
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