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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 |
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ltd.2 |
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nltled.1 |
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Ref | Expression |
---|---|
nltled |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nltled.1 |
. 2
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2 | ltd.1 |
. . 3
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3 | ltd.2 |
. . 3
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4 | 2, 3 | lenltd 8104 |
. 2
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5 | 1, 4 | mpbird 167 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-xr 8025 df-le 8027 |
This theorem is referenced by: ltntri 8114 suprubex 8937 infregelbex 9627 cvgratz 11571 zsupcl 11979 zssinfcl 11980 infssuzledc 11982 dvdslegcd 11996 pw2dvdseulemle 12198 dedekindeulemuub 14547 dedekindeulemlu 14551 suplociccex 14555 dedekindicclemuub 14556 dedekindicclemlu 14560 ivthinclemlopn 14566 ivthinclemuopn 14568 refeq 15230 |
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