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Mirrors > Home > ILE Home > Th. List > eluzle | Unicode version |
Description: Implication of membership in an upper set of integers. (Contributed by NM, 6-Sep-2005.) |
Ref | Expression |
---|---|
eluzle |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluz2 9325 | . 2 | |
2 | 1 | simp3bi 998 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 class class class wbr 3924 cfv 5118 cle 7794 cz 9047 cuz 9319 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-cnex 7704 ax-resscn 7705 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fv 5126 df-ov 5770 df-neg 7929 df-z 9048 df-uz 9320 |
This theorem is referenced by: uztrn 9335 uzneg 9337 uzss 9339 uz11 9341 eluzp1l 9343 uzm1 9349 uzin 9351 uzind4 9376 elfz5 9791 elfzle1 9800 elfzle2 9801 elfzle3 9803 uzsplit 9865 uzdisj 9866 uznfz 9876 elfz2nn0 9885 uzsubfz0 9899 nn0disj 9908 fzouzdisj 9950 elfzonelfzo 10000 mulp1mod1 10131 m1modge3gt1 10137 uzennn 10202 seq3split 10245 seq3f1olemqsumk 10265 seq3f1o 10270 seq3coll 10578 seq3shft 10603 cvg1nlemcau 10749 resqrexlemcvg 10784 resqrexlemga 10788 summodclem2a 11143 fsum3 11149 fsum3cvg3 11158 fsumadd 11168 sumsnf 11171 fsummulc2 11210 isumshft 11252 divcnv 11259 geolim2 11274 cvgratnnlemseq 11288 cvgratnnlemsumlt 11290 cvgratz 11294 mertenslemi1 11297 efcllemp 11353 infssuzex 11631 dvdsbnd 11634 ncoprmgcdne1b 11759 hashdvds 11886 cvgcmp2nlemabs 13216 |
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