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Mirrors > Home > ILE Home > Th. List > 0nn0 | Unicode version |
Description: 0 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
0nn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2040 | . 2 | |
2 | elnn0 8183 | . . . 4 | |
3 | 2 | biimpri 124 | . . 3 |
4 | 3 | olcs 655 | . 2 |
5 | 1, 4 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 629 wceq 1243 wcel 1393 cc0 6889 cn 7914 cn0 8181 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-mulcl 6982 ax-i2m1 6989 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-n0 8182 |
This theorem is referenced by: elnn0z 8258 nn0ind-raph 8355 numlti 8391 nummul1c 8403 decaddc2 8410 decaddi 8411 decaddci 8412 decaddci2 8413 6p5e11 8417 7p4e11 8419 8p3e11 8423 9p2e11 8429 10p10e20 8437 0elfz 8977 4fvwrd4 8997 fvinim0ffz 9096 exple1 9310 nn0seqcvgd 9880 ialgcvg 9887 |
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