Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fzssuz | GIF version |
Description: A finite set of sequential integers is a subset of an upper set of integers. (Contributed by NM, 28-Oct-2005.) |
Ref | Expression |
---|---|
fzssuz | ⊢ (𝑀...𝑁) ⊆ (ℤ≥‘𝑀) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzuz 9041 | . 2 ⊢ (𝑘 ∈ (𝑀...𝑁) → 𝑘 ∈ (ℤ≥‘𝑀)) | |
2 | 1 | ssriv 3003 | 1 ⊢ (𝑀...𝑁) ⊆ (ℤ≥‘𝑀) |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2973 ‘cfv 4922 (class class class)co 5532 ℤ≥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: fzossnn0 9184 iseqcaopr2 9461 isprm3 10500 2prm 10509 |
Copyright terms: Public domain | W3C validator |