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Mirrors > Home > ILE Home > Th. List > elfzuz | Unicode version |
Description: A member of a finite set of sequential integers belongs to an upper set of integers. (Contributed by NM, 17-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
elfzuz |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzuzb 10019 |
. 2
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2 | 1 | simplbi 274 |
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-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4122 ax-pow 4175 ax-pr 4210 ax-setind 4537 ax-cnex 7902 ax-resscn 7903 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2740 df-sbc 2964 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-opab 4066 df-mpt 4067 df-id 4294 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-ima 4640 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-fv 5225 df-ov 5878 df-oprab 5879 df-mpo 5880 df-neg 8131 df-z 9254 df-uz 9529 df-fz 10009 |
This theorem is referenced by: elfzel1 10024 elfzelz 10025 elfzle1 10027 eluzfz2b 10033 fzsplit2 10050 fzsplit 10051 fzopth 10061 fzss1 10063 fzss2 10064 fzssuz 10065 fzp1elp1 10075 uzsplit 10092 elfzmlbm 10131 fzosplit 10177 seq3feq2 10470 seq3feq 10472 ser3mono 10478 seq3caopr3 10481 iseqf1olemkle 10484 iseqf1olemklt 10485 iseqf1olemnab 10488 iseqf1olemqk 10494 iseqf1olemjpcl 10495 iseqf1olemqpcl 10496 iseqf1olemfvp 10497 seq3f1olemqsumkj 10498 seq3f1olemqsumk 10499 seq3f1olemqsum 10500 seq3f1olemstep 10501 seq3f1oleml 10503 seq3f1o 10504 seq3z 10511 ser0 10514 ser3le 10518 seq3coll 10822 climub 11352 sumrbdclem 11385 fsum3cvg 11386 fsum3ser 11405 fsump1i 11441 fsum0diaglem 11448 iserabs 11483 isumsplit 11499 isum1p 11500 geosergap 11514 mertenslemi1 11543 prodf1 11550 prodfap0 11553 prodfrecap 11554 prodfdivap 11555 prodrbdclem 11579 fproddccvg 11580 fprodntrivap 11592 fprodabs 11624 fprodeq0 11625 infssuzex 11950 prmind2 12120 prmdvdsfz 12139 isprm5lem 12141 eulerthlemrprm 12229 eulerthlema 12230 pcfac 12348 lgsdilem2 14440 cvgcmp2nlemabs 14783 |
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