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Mirrors > Home > ILE Home > Th. List > 1on | Unicode version |
Description: Ordinal 1 is an ordinal number. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1on |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 6384 | . 2 | |
2 | 0elon 4370 | . . 3 | |
3 | 2 | onsuci 4493 | . 2 |
4 | 1, 3 | eqeltri 2239 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2136 c0 3409 con0 4341 csuc 4343 c1o 6377 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-13 2138 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-nul 4108 ax-pow 4153 ax-pr 4187 ax-un 4411 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-dif 3118 df-un 3120 df-in 3122 df-ss 3129 df-nul 3410 df-pw 3561 df-sn 3582 df-pr 3583 df-uni 3790 df-tr 4081 df-iord 4344 df-on 4346 df-suc 4349 df-1o 6384 |
This theorem is referenced by: 1oex 6392 2on 6393 2on0 6394 2oconcl 6407 fnoei 6420 oeiexg 6421 oeiv 6424 oei0 6427 oeicl 6430 o1p1e2 6436 oawordriexmid 6438 enpr2d 6783 endisj 6790 snexxph 6915 djuex 7008 1stinr 7041 2ndinr 7042 pm54.43 7146 xpdjuen 7174 prarloclemarch2 7360 bj-el2oss1o 13665 nnsf 13895 |
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