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Mirrors > Home > ILE Home > Th. List > nn0ex | Unicode version |
Description: The set of nonnegative integers exists. (Contributed by NM, 18-Jul-2004.) |
Ref | Expression |
---|---|
nn0ex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-n0 8289 | . 2 | |
2 | nnex 8045 | . . 3 | |
3 | c0ex 7113 | . . . 4 | |
4 | 3 | snex 3957 | . . 3 |
5 | 2, 4 | unex 4194 | . 2 |
6 | 1, 5 | eqeltri 2151 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1433 cvv 2601 cun 2971 csn 3398 cc0 6981 cn 8039 cn0 8288 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-cnex 7067 ax-resscn 7068 ax-1cn 7069 ax-1re 7070 ax-icn 7071 ax-addcl 7072 ax-addrcl 7073 ax-mulcl 7074 ax-i2m1 7081 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-uni 3602 df-int 3637 df-inn 8040 df-n0 8289 |
This theorem is referenced by: nn0ennn 9425 nnenom 9426 eucialgcvga 10440 eucialg 10441 |
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