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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 7873 | . 2 |
5 | 1, 4 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 1480 class class class wbr 3924 cr 7612 clt 7793 cle 7794 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-cnv 4542 df-xr 7797 df-le 7799 |
This theorem is referenced by: ltntri 7883 suprubex 8702 cvgratz 11294 zsupcl 11629 zssinfcl 11630 infssuzledc 11632 dvdslegcd 11642 pw2dvdseulemle 11834 dedekindeulemuub 12753 dedekindeulemlu 12757 suplociccex 12761 dedekindicclemuub 12762 dedekindicclemlu 12766 ivthinclemlopn 12772 ivthinclemuopn 12774 refeq 13212 |
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