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Mirrors > Home > ILE Home > Th. List > nnnn0 | Unicode version |
Description: A positive integer is a nonnegative integer. (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nnnn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssnn0 8184 | . 2 | |
2 | 1 | sseli 2941 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 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 |
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-in 2924 df-ss 2931 df-n0 8182 |
This theorem is referenced by: nnnn0i 8189 elnnnn0b 8226 elnnnn0c 8227 elnn0z 8258 elz2 8312 nn0ind-raph 8355 zindd 8356 fzo1fzo0n0 9039 ubmelfzo 9056 elfzom1elp1fzo 9058 fzo0sn0fzo1 9077 modqmulnn 9184 expnegap0 9263 expcllem 9266 expcl2lemap 9267 expap0 9285 expeq0 9286 mulexpzap 9295 expnlbnd 9373 resqrexlemlo 9611 absexpzap 9676 |
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