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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7005 | . 2 | |
2 | zsscn 8253 | . 2 | |
3 | 1, 2 | ssexi 3895 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 cc 6887 cz 8245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-cnex 6975 ax-resscn 6976 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-rab 2315 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-neg 7185 df-z 8246 |
This theorem is referenced by: dfuzi 8348 uzval 8475 uzf 8476 fzval 8876 fzf 8878 flval 9116 frec2uzzd 9186 frec2uzsucd 9187 frec2uzrand 9191 frec2uzf1od 9192 frecuzrdgrrn 9194 frec2uzrdg 9195 frecuzrdgrom 9196 frecuzrdgsuc 9201 frecfzennn 9203 climz 9813 iserclim0 9826 climaddc1 9849 climmulc2 9851 climsubc1 9852 climsubc2 9853 climle 9854 climlec2 9861 |
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