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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 7712 | . 2 | |
2 | zsscn 9030 | . 2 | |
3 | 1, 2 | ssexi 4036 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 cc 7586 cz 9022 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-neg 7904 df-z 9023 |
This theorem is referenced by: dfuzi 9129 uzval 9296 uzf 9297 fzval 9760 fzf 9762 flval 10013 frec2uzrand 10146 frec2uzf1od 10147 frecfzennn 10167 uzennn 10177 hashinfom 10492 climz 11029 serclim0 11042 climaddc1 11066 climmulc2 11068 climsubc1 11069 climsubc2 11070 climle 11071 climlec2 11078 iserabs 11212 isumshft 11227 explecnv 11242 qnumval 11790 qdenval 11791 znnen 11838 exmidunben 11866 qnnen 11871 lmres 12344 climcncf 12667 |
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