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Mirrors > Home > ILE Home > Th. List > nltled | Unicode version |
Description: 'Not less than ' implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
ltd.1 | |
ltd.2 | |
nltled.1 |
Ref | Expression |
---|---|
nltled |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nltled.1 | . 2 | |
2 | ltd.1 | . . 3 | |
3 | ltd.2 | . . 3 | |
4 | 2, 3 | lenltd 7227 | . 2 |
5 | 1, 4 | mpbird 165 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 1433 class class class wbr 3785 cr 6980 clt 7153 cle 7154 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-xr 7157 df-le 7159 |
This theorem is referenced by: suprubex 8029 zsupcl 10343 zssinfcl 10344 infssuzledc 10346 dvdslegcd 10356 pw2dvdseulemle 10545 |
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