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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 |
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ltd.2 |
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Ref | Expression |
---|---|
lenltd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 |
. 2
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2 | ltd.2 |
. 2
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3 | lenlt 7864 |
. 2
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4 | 1, 2, 3 | syl2anc 409 |
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-in1 604 ax-in2 605 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 |
This theorem depends on definitions: df-bi 116 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-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-xr 7828 df-le 7830 |
This theorem is referenced by: ltnsymd 7906 nltled 7907 lensymd 7908 leadd1 8216 lemul1 8379 leltap 8411 ap0gt0 8426 prodgt0 8634 prodge0 8636 lediv1 8651 lemuldiv 8663 lerec 8666 lt2msq 8668 le2msq 8683 squeeze0 8686 suprleubex 8736 0mnnnnn0 9033 elnn0z 9091 uzm1 9380 fztri3or 9850 fzdisj 9863 uzdisj 9904 nn0disj 9946 fzouzdisj 9988 elfzonelfzo 10038 flqeqceilz 10122 modifeq2int 10190 modsumfzodifsn 10200 expcanlem 10493 fimaxq 10605 resqrexlemoverl 10825 leabs 10878 absle 10893 maxleast 11017 minmax 11033 climge0 11126 cxple 13045 |
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