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Mirrors > Home > ILE Home > Th. List > 2on0 | Unicode version |
Description: Ordinal two is not zero. (Contributed by Scott Fenton, 17-Jun-2011.) |
Ref | Expression |
---|---|
2on0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 6377 | . 2 | |
2 | 1on 6383 | . . 3 | |
3 | nsuceq0g 4391 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqnetri 2357 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 wne 2334 c0 3405 con0 4336 csuc 4338 c1o 6369 c2o 6370 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-nul 4103 ax-pow 4148 ax-pr 4182 ax-un 4406 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-v 2724 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-nul 3406 df-pw 3556 df-sn 3577 df-pr 3578 df-uni 3785 df-tr 4076 df-iord 4339 df-on 4341 df-suc 4344 df-1o 6376 df-2o 6377 |
This theorem is referenced by: snnen2oprc 6818 prarloclemcalc 7435 pwle2 13739 |
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