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Mirrors > Home > ILE Home > Th. List > zex | Unicode version |
Description: The set of integers exists. (Contributed by NM, 30-Jul-2004.) (Revised by Mario Carneiro, 17-Nov-2014.) |
Ref | Expression |
---|---|
zex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7527 |
. 2
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2 | zsscn 8819 |
. 2
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3 | 1, 2 | ssexi 3983 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-cnex 7497 ax-resscn 7498 |
This theorem depends on definitions: df-bi 116 df-3or 926 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-rab 2369 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-iota 4993 df-fv 5036 df-ov 5669 df-neg 7717 df-z 8812 |
This theorem is referenced by: dfuzi 8917 uzval 9082 uzf 9083 fzval 9487 fzf 9489 flval 9740 frec2uzrand 9873 frec2uzf1od 9874 frecfzennn 9894 hashinfom 10247 climz 10741 serclim0 10754 iserclim0 10755 climaddc1 10778 climmulc2 10780 climsubc1 10781 climsubc2 10782 climle 10783 climlec2 10791 iserabs 10930 isumshft 10945 explecnv 10960 qnumval 11502 qdenval 11503 znnen 11550 climcncf 11913 |
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