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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 8024 | . 2 |
5 | 1, 4 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 2141 class class class wbr 3987 cr 7760 clt 7941 cle 7942 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-xp 4615 df-cnv 4617 df-xr 7945 df-le 7947 |
This theorem is referenced by: ltntri 8034 suprubex 8854 infregelbex 9544 cvgratz 11482 zsupcl 11889 zssinfcl 11890 infssuzledc 11892 dvdslegcd 11906 pw2dvdseulemle 12108 dedekindeulemuub 13348 dedekindeulemlu 13352 suplociccex 13356 dedekindicclemuub 13357 dedekindicclemlu 13361 ivthinclemlopn 13367 ivthinclemuopn 13369 refeq 14020 |
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