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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 7953 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wcel 2128 class class class wbr 3965 cr 7731 clt 7912 cle 7913 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-xp 4592 df-cnv 4594 df-xr 7916 df-le 7918 |
This theorem is referenced by: ltnsymd 7995 nltled 7996 lensymd 7997 leadd1 8305 lemul1 8468 leltap 8500 ap0gt0 8515 prodgt0 8723 prodge0 8725 lediv1 8740 lemuldiv 8752 lerec 8755 lt2msq 8757 le2msq 8772 squeeze0 8775 suprleubex 8825 0mnnnnn0 9122 elnn0z 9180 uzm1 9469 infregelbex 9509 fztri3or 9941 fzdisj 9954 uzdisj 9995 nn0disj 10037 fzouzdisj 10079 elfzonelfzo 10129 flqeqceilz 10217 modifeq2int 10285 modsumfzodifsn 10295 expcanlem 10589 fimaxq 10701 resqrexlemoverl 10921 leabs 10974 absle 10989 maxleast 11113 minmax 11129 climge0 11222 cxple 13237 |
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