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Mirrors > Home > ILE Home > Th. List > zltlem1 | Unicode version |
Description: Integer ordering relation. (Contributed by NM, 13-Nov-2004.) |
Ref | Expression |
---|---|
zltlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peano2zm 9326 |
. . 3
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2 | zleltp1 9343 |
. . 3
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3 | 1, 2 | sylan2 286 |
. 2
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4 | zcn 9293 |
. . . . 5
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5 | ax-1cn 7939 |
. . . . 5
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6 | npcan 8201 |
. . . . 5
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7 | 4, 5, 6 | sylancl 413 |
. . . 4
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8 | 7 | adantl 277 |
. . 3
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9 | 8 | breq2d 4033 |
. 2
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10 | 3, 9 | bitr2d 189 |
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-in1 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 ax-un 4454 ax-setind 4557 ax-cnex 7937 ax-resscn 7938 ax-1cn 7939 ax-1re 7940 ax-icn 7941 ax-addcl 7942 ax-addrcl 7943 ax-mulcl 7944 ax-addcom 7946 ax-addass 7948 ax-distr 7950 ax-i2m1 7951 ax-0lt1 7952 ax-0id 7954 ax-rnegex 7955 ax-cnre 7957 ax-pre-ltirr 7958 ax-pre-ltwlin 7959 ax-pre-lttrn 7960 ax-pre-ltadd 7962 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 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-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-int 3863 df-br 4022 df-opab 4083 df-id 4314 df-xp 4653 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-iota 5199 df-fun 5240 df-fv 5246 df-riota 5855 df-ov 5903 df-oprab 5904 df-mpo 5905 df-pnf 8029 df-mnf 8030 df-xr 8031 df-ltxr 8032 df-le 8033 df-sub 8165 df-neg 8166 df-inn 8955 df-n0 9212 df-z 9289 |
This theorem is referenced by: nn0ltlem1 9352 nn0lt2 9369 nn0le2is012 9370 nnltlem1 9373 nnm1ge0 9374 zextlt 9380 uzm1 9594 elfzm11 10127 elfzo 10185 fzosplitprm1 10270 intfracq 10357 iseqf1olemqcl 10525 iseqf1olemnab 10527 iseqf1olemab 10528 seq3f1olemqsumkj 10537 seq3f1olemqsum 10539 seq3coll 10863 fzm1ndvds 11903 nn0seqcvgd 12084 isprm3 12161 isprm5lem 12184 isprm5 12185 pw2dvds 12209 prmdiveq 12279 4sqlem12 12445 wilthlem1 14883 lgseisenlem2 14937 2sqlem8 14956 |
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