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Mirrors > Home > ILE Home > Th. List > nnex | Unicode version |
Description: The set of positive integers exists. (Contributed by NM, 3-Oct-1999.) (Revised by Mario Carneiro, 17-Nov-2014.) |
Ref | Expression |
---|---|
nnex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7898 | . 2 | |
2 | nnsscn 8883 | . 2 | |
3 | 1, 2 | ssexi 4127 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 cvv 2730 cc 7772 cn 8878 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sep 4107 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-in 3127 df-ss 3134 df-int 3832 df-inn 8879 |
This theorem is referenced by: nn0ex 9141 nn0ennn 10389 climrecvg1n 11311 climcvg1nlem 11312 divcnv 11460 trireciplem 11463 expcnvap0 11465 expcnv 11467 geo2lim 11479 prmex 12067 qnumval 12139 qdenval 12140 oddennn 12347 evenennn 12348 xpnnen 12349 znnen 12353 qnnen 12386 ssnnctlemct 12401 nninfdc 12408 ndxarg 12439 trilpo 14075 redcwlpo 14087 nconstwlpo 14097 neapmkv 14099 |
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