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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 7744 | . 2 | |
2 | nnsscn 8725 | . 2 | |
3 | 1, 2 | ssexi 4066 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2686 cc 7618 cn 8720 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-cnex 7711 ax-resscn 7712 ax-1re 7714 ax-addrcl 7717 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-in 3077 df-ss 3084 df-int 3772 df-inn 8721 |
This theorem is referenced by: nn0ex 8983 nn0ennn 10206 climrecvg1n 11117 climcvg1nlem 11118 divcnv 11266 trireciplem 11269 expcnvap0 11271 expcnv 11273 geo2lim 11285 prmex 11794 qnumval 11863 qdenval 11864 oddennn 11905 evenennn 11906 xpnnen 11907 znnen 11911 qnnen 11944 ndxarg 11982 trilpo 13236 |
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