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Mirrors > Home > ILE Home > Th. List > elfzelz | Unicode version |
Description: A member of a finite set of sequential integer is an integer. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
elfzelz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzuz 9041 | . 2 | |
2 | eluzelz 8628 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cfv 4922 (class class class)co 5532 cz 8351 cuz 8619 cfz 9029 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-setind 4280 ax-cnex 7067 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-sbc 2816 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-fv 4930 df-ov 5535 df-oprab 5536 df-mpt2 5537 df-neg 7282 df-z 8352 df-uz 8620 df-fz 9030 |
This theorem is referenced by: elfz1eq 9054 fzsplit2 9069 fzdisj 9071 elfznn 9073 fznatpl1 9093 fzdifsuc 9098 fzrev2i 9103 fzrev3i 9105 elfzp12 9116 fznuz 9119 fzrevral 9122 fzshftral 9125 fznn0sub2 9139 elfzmlbm 9142 difelfznle 9146 fzosplit 9186 isermono 9457 bcval2 9677 bcval4 9679 bccmpl 9681 bcp1nk 9689 bcpasc 9693 bccl2 9695 fzm1ndvds 10256 lcmval 10445 lcmcllem 10449 lcmledvds 10452 prmdvdsfz 10520 |
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