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Mirrors > Home > ILE Home > Th. List > lenltd | Unicode version |
Description: 'Less than or equal to' in terms of 'less than'. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
ltd.1 | |
ltd.2 |
Ref | Expression |
---|---|
lenltd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 | . 2 | |
2 | ltd.2 | . 2 | |
3 | lenlt 7094 | . 2 | |
4 | 1, 2, 3 | syl2anc 391 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 98 wcel 1393 class class class wbr 3764 cr 6888 clt 7060 cle 7061 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-xr 7064 df-le 7066 |
This theorem is referenced by: ltnsymd 7136 leadd1 7425 lemul1 7584 leltap 7615 ap0gt0 7629 prodgt0 7818 prodge0 7820 lediv1 7835 lemuldiv 7847 lerec 7850 lt2msq 7852 le2msq 7867 squeeze0 7870 0mnnnnn0 8214 elnn0z 8258 uzm1 8503 fztri3or 8903 fzdisj 8916 uzdisj 8955 nn0disj 8995 fzouzdisj 9036 elfzonelfzo 9086 flqeqceilz 9160 expival 9257 resqrexlemoverl 9619 leabs 9672 absle 9685 climge0 9845 |
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