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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 9770 | . 2 | |
2 | eluzelz 9303 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cfv 5093 (class class class)co 5742 cz 9022 cuz 9294 cfz 9758 |
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-in1 588 ax-in2 589 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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-neg 7904 df-z 9023 df-uz 9295 df-fz 9759 |
This theorem is referenced by: elfz1eq 9783 fzsplit2 9798 fzdisj 9800 elfznn 9802 fznatpl1 9824 fzdifsuc 9829 fzrev2i 9834 fzrev3i 9836 elfzp12 9847 fznuz 9850 fzrevral 9853 fzshftral 9856 fznn0sub2 9873 elfzmlbm 9876 difelfznle 9880 fzosplit 9922 ser3mono 10219 iseqf1olemkle 10225 iseqf1olemklt 10226 iseqf1olemqcl 10227 iseqf1olemnab 10229 iseqf1olemab 10230 iseqf1olemmo 10233 iseqf1olemqk 10235 seq3f1olemqsumkj 10239 seq3f1olemqsumk 10240 seq3f1olemqsum 10241 seq3f1olemstep 10242 bcval2 10464 bcval4 10466 bccmpl 10468 bcp1nk 10476 bcpasc 10480 bccl2 10482 zfz1isolemiso 10550 seq3coll 10553 seq3shft 10578 sumrbdclem 11113 summodclem2a 11118 fsum0diaglem 11177 fisum0diag 11178 mptfzshft 11179 fsumrev 11180 fsumshft 11181 fsumshftm 11182 fisum0diag2 11184 binomlem 11220 binom11 11223 bcxmas 11226 arisum 11235 geo2sum 11251 cvgratnnlemabsle 11264 cvgratnnlemrate 11267 mertenslemub 11271 mertenslemi1 11272 fzm1ndvds 11481 lcmval 11671 lcmcllem 11675 lcmledvds 11678 prmdvdsfz 11746 phivalfi 11815 hashdvds 11824 phiprmpw 11825 trilpolemlt1 13161 supfz 13164 inffz 13165 |
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