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| Mirrors > Home > ILE Home > Th. List > fzss2 | Unicode version | ||
| Description: Subset relationship for finite sets of sequential integers. (Contributed by NM, 4-Oct-2005.) (Revised by Mario Carneiro, 30-Apr-2015.) |
| Ref | Expression |
|---|---|
| fzss2 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz 10142 |
. . . . 5
| |
| 2 | 1 | adantl 277 |
. . . 4
|
| 3 | elfzuz3 10143 |
. . . . 5
| |
| 4 | uztrn 9664 |
. . . . 5
| |
| 5 | 3, 4 | sylan2 286 |
. . . 4
|
| 6 | elfzuzb 10140 |
. . . 4
| |
| 7 | 2, 5, 6 | sylanbrc 417 |
. . 3
|
| 8 | 7 | ex 115 |
. 2
|
| 9 | 8 | ssrdv 3198 |
1
|
| 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 615 ax-in2 616 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-13 2177 ax-14 2178 ax-ext 2186 ax-sep 4161 ax-pow 4217 ax-pr 4252 ax-un 4479 ax-setind 4584 ax-cnex 8015 ax-resscn 8016 ax-pre-ltwlin 8037 |
| This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1375 df-fal 1378 df-nf 1483 df-sb 1785 df-eu 2056 df-mo 2057 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ne 2376 df-nel 2471 df-ral 2488 df-rex 2489 df-rab 2492 df-v 2773 df-sbc 2998 df-dif 3167 df-un 3169 df-in 3171 df-ss 3178 df-pw 3617 df-sn 3638 df-pr 3639 df-op 3641 df-uni 3850 df-br 4044 df-opab 4105 df-mpt 4106 df-id 4339 df-xp 4680 df-rel 4681 df-cnv 4682 df-co 4683 df-dm 4684 df-rn 4685 df-res 4686 df-ima 4687 df-iota 5231 df-fun 5272 df-fn 5273 df-f 5274 df-fv 5278 df-ov 5946 df-oprab 5947 df-mpo 5948 df-pnf 8108 df-mnf 8109 df-xr 8110 df-ltxr 8111 df-le 8112 df-neg 8245 df-z 9372 df-uz 9648 df-fz 10130 |
| This theorem is referenced by: fzssp1 10188 elfz0add 10241 fzoss2 10294 seqsplitg 10632 seqcaopr2g 10637 iseqf1olemnab 10644 seqf1oglem2a 10661 seqf1oglem2 10663 seqhomog 10673 bcm1k 10903 seq3coll 10985 fsum0diaglem 11722 fisum0diag2 11729 mertenslemi1 11817 prodfrecap 11828 pcfac 12644 strleund 12906 strleun 12907 strext 12908 plyaddlem1 15190 plymullem1 15191 plycoeid3 15200 gausslemma2dlem2 15510 lgsquadlem3 15527 |
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