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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0le1 8211 | . . 3 | |
2 | 1re 7733 | . . . 4 | |
3 | 2, 2 | addge0i 8219 | . . 3 |
4 | 1, 1, 3 | mp2an 422 | . 2 |
5 | df-2 8747 | . 2 | |
6 | 4, 5 | breqtrri 3925 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3899 (class class class)co 5742 cc0 7588 c1 7589 caddc 7591 cle 7769 c2 8739 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-addcom 7688 ax-addass 7690 ax-i2m1 7693 ax-0lt1 7694 ax-0id 7696 ax-rnegex 7697 ax-pre-ltirr 7700 ax-pre-ltwlin 7701 ax-pre-lttrn 7702 ax-pre-ltadd 7704 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-nel 2381 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-iota 5058 df-fv 5101 df-ov 5745 df-pnf 7770 df-mnf 7771 df-xr 7772 df-ltxr 7773 df-le 7774 df-2 8747 |
This theorem is referenced by: expubnd 10318 4bc2eq6 10488 sqrt4 10787 sqrt2gt1lt2 10789 amgm2 10858 bdtrilem 10978 ege2le3 11304 cos2bnd 11394 evennn2n 11507 6gcd4e2 11610 sqrt2irrlem 11766 sqrt2irraplemnn 11784 oddennn 11832 sincos4thpi 12848 |
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