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Mirrors > Home > ILE Home > Th. List > eluzfz2 | Unicode version |
Description: Membership in a finite set of sequential integers - special case. (Contributed by NM, 13-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
eluzfz2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzelz 9018 |
. . 3
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2 | uzid 9023 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | eluzfz 9425 |
. 2
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5 | 3, 4 | mpdan 412 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-pow 4007 ax-pr 4034 ax-un 4258 ax-setind 4351 ax-cnex 7426 ax-resscn 7427 ax-pre-ltirr 7447 |
This theorem depends on definitions: df-bi 115 df-3or 925 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-nel 2351 df-ral 2364 df-rex 2365 df-rab 2368 df-v 2621 df-sbc 2841 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-pw 3429 df-sn 3450 df-pr 3451 df-op 3453 df-uni 3652 df-br 3844 df-opab 3898 df-mpt 3899 df-id 4118 df-xp 4442 df-rel 4443 df-cnv 4444 df-co 4445 df-dm 4446 df-rn 4447 df-res 4448 df-ima 4449 df-iota 4975 df-fun 5012 df-fn 5013 df-f 5014 df-fv 5018 df-ov 5647 df-oprab 5648 df-mpt2 5649 df-pnf 7514 df-mnf 7515 df-xr 7516 df-ltxr 7517 df-le 7518 df-neg 7646 df-z 8741 df-uz 9010 df-fz 9415 |
This theorem is referenced by: eluzfz2b 9437 elfzubelfz 9440 fzopth 9464 fzsuc 9471 fseq1p1m1 9496 fzm1 9502 fzneuz 9503 fzoend 9621 exfzdc 9639 uzsinds 9836 seq3clss 9875 iseqfveq2 9878 seq3fveq2 9880 iseqshft2 9886 monoord 9892 monoord2 9893 seq3split 9895 iseqsplit 9896 iseqcaopr3 9898 seq3f1olemp 9919 iseqid3s 9926 seq3id2 9928 iseqid2 9929 ser3ge0 9940 iseqcoll 10235 isummolem2a 10758 fsumm1 10797 telfsumo 10847 telfsumo2 10848 fsumparts 10851 supfz 11799 |
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