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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 7965 |
. 2
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2 | zsscn 9291 |
. 2
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3 | 1, 2 | ssexi 4156 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7932 ax-resscn 7933 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 df-neg 8161 df-z 9284 |
This theorem is referenced by: dfuzi 9393 uzval 9560 uzf 9561 fzval 10040 fzf 10042 flval 10303 frec2uzrand 10436 frec2uzf1od 10437 frecfzennn 10457 uzennn 10467 hashinfom 10790 climz 11332 serclim0 11345 climaddc1 11369 climmulc2 11371 climsubc1 11372 climsubc2 11373 climle 11374 climlec2 11381 iserabs 11515 isumshft 11530 explecnv 11545 prodfclim1 11584 qnumval 12217 qdenval 12218 odzval 12273 znnen 12449 exmidunben 12477 qnnen 12482 mulgfvalg 13063 mulgex 13065 zringplusg 13896 zringmulr 13898 zringmpg 13905 zrhval2 13916 lmres 14208 climcncf 14531 |
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