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Mirrors > Home > ILE Home > Th. List > 0le2 | Unicode version |
Description: 0 is less than or equal to 2. (Contributed by David A. Wheeler, 7-Dec-2018.) |
Ref | Expression |
---|---|
0le2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0le1 8162 |
. . 3
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2 | 1re 7689 |
. . . 4
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3 | 2, 2 | addge0i 8170 |
. . 3
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4 | 1, 1, 3 | mp2an 420 |
. 2
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5 | df-2 8689 |
. 2
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6 | 4, 5 | breqtrri 3920 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 3895 (class class class)co 5728
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This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-13 1474 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 ax-un 4315 ax-setind 4412 ax-cnex 7636 ax-resscn 7637 ax-1cn 7638 ax-1re 7639 ax-icn 7640 ax-addcl 7641 ax-addrcl 7642 ax-mulcl 7643 ax-addcom 7645 ax-addass 7647 ax-i2m1 7650 ax-0lt1 7651 ax-0id 7653 ax-rnegex 7654 ax-pre-ltirr 7657 ax-pre-ltwlin 7658 ax-pre-lttrn 7659 ax-pre-ltadd 7661 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-fal 1320 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ne 2283 df-nel 2378 df-ral 2395 df-rex 2396 df-rab 2399 df-v 2659 df-dif 3039 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-br 3896 df-opab 3950 df-xp 4505 df-cnv 4507 df-iota 5046 df-fv 5089 df-ov 5731 df-pnf 7726 df-mnf 7727 df-xr 7728 df-ltxr 7729 df-le 7730 df-2 8689 |
This theorem is referenced by: expubnd 10243 4bc2eq6 10413 sqrt4 10711 sqrt2gt1lt2 10713 amgm2 10782 bdtrilem 10902 ege2le3 11228 cos2bnd 11318 evennn2n 11428 6gcd4e2 11529 sqrt2irrlem 11685 sqrt2irraplemnn 11702 oddennn 11750 |
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