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Mirrors > Home > ILE Home > Th. List > eluz1 | Unicode version |
Description: Membership in the upper set of integers starting at . (Contributed by NM, 5-Sep-2005.) |
Ref | Expression |
---|---|
eluz1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uzval 9296 | . . 3 | |
2 | 1 | eleq2d 2187 | . 2 |
3 | breq2 3903 | . . 3 | |
4 | 3 | elrab 2813 | . 2 |
5 | 2, 4 | syl6bb 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 1465 crab 2397 class class class wbr 3899 cfv 5093 cle 7769 cz 9022 cuz 9294 |
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-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-cnex 7679 ax-resscn 7680 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 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-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 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-iota 5058 df-fun 5095 df-fv 5101 df-ov 5745 df-neg 7904 df-z 9023 df-uz 9295 |
This theorem is referenced by: eluz2 9300 eluz1i 9301 eluz 9307 uzid 9308 uzss 9314 eluzp1m1 9317 eluzadd 9322 eluzsub 9323 raluz 9341 rexuz 9343 caucvgrelemcau 10720 caucvgre 10721 algcvga 11659 |
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