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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 9356 |
. 2
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2 | 1 | simp3bi 999 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-cnex 7735 ax-resscn 7736 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 df-ov 5785 df-neg 7960 df-z 9079 df-uz 9351 |
This theorem is referenced by: uztrn 9366 uzneg 9368 uzss 9370 uz11 9372 eluzp1l 9374 uzm1 9380 uzin 9382 uzind4 9410 elfz5 9829 elfzle1 9838 elfzle2 9839 elfzle3 9841 uzsplit 9903 uzdisj 9904 uznfz 9914 elfz2nn0 9923 uzsubfz0 9937 nn0disj 9946 fzouzdisj 9988 elfzonelfzo 10038 mulp1mod1 10169 m1modge3gt1 10175 uzennn 10240 seq3split 10283 seq3f1olemqsumk 10303 seq3f1o 10308 seq3coll 10617 seq3shft 10642 cvg1nlemcau 10788 resqrexlemcvg 10823 resqrexlemga 10827 summodclem2a 11182 fsum3 11188 fsum3cvg3 11197 fsumadd 11207 sumsnf 11210 fsummulc2 11249 isumshft 11291 divcnv 11298 geolim2 11313 cvgratnnlemseq 11327 cvgratnnlemsumlt 11329 cvgratz 11333 mertenslemi1 11336 prodmodclem3 11376 prodmodclem2a 11377 efcllemp 11401 infssuzex 11678 dvdsbnd 11681 ncoprmgcdne1b 11806 hashdvds 11933 cvgcmp2nlemabs 13402 |
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