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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluz2 9564 |
. 2
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2 | 1 | simp3bi 1016 |
1
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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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-cnex 7932 ax-resscn 7933 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-fv 5243 df-ov 5899 df-neg 8161 df-z 9284 df-uz 9559 |
This theorem is referenced by: uztrn 9574 uzneg 9576 uzss 9578 uz11 9580 eluzp1l 9582 uzm1 9588 uzin 9590 uzind4 9618 elfz5 10047 elfzle1 10057 elfzle2 10058 elfzle3 10060 uzsplit 10122 uzdisj 10123 uznfz 10133 elfz2nn0 10142 uzsubfz0 10159 nn0disj 10168 fzouzdisj 10210 elfzonelfzo 10260 mulp1mod1 10396 m1modge3gt1 10402 uzennn 10467 seq3split 10510 seq3f1olemqsumk 10530 seq3f1o 10535 seq3coll 10854 seq3shft 10879 cvg1nlemcau 11025 resqrexlemcvg 11060 resqrexlemga 11064 summodclem2a 11421 fsum3 11427 fsum3cvg3 11436 fsumadd 11446 sumsnf 11449 fsummulc2 11488 isumshft 11530 divcnv 11537 geolim2 11552 cvgratnnlemseq 11566 cvgratnnlemsumlt 11568 cvgratz 11572 mertenslemi1 11575 prodmodclem3 11615 prodmodclem2a 11616 fprodntrivap 11624 prodsnf 11632 fprodeq0 11657 efcllemp 11698 infssuzex 11982 suprzubdc 11985 dvdsbnd 11989 uzwodc 12070 ncoprmgcdne1b 12121 isprm5 12174 hashdvds 12253 pcmpt2 12376 pcfaclem 12381 pcfac 12382 nninfdclemp1 12501 strext 12617 lgslem1 14859 lgsdirprm 14893 cvgcmp2nlemabs 15239 |
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