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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 8452 |
. . 3
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2 | 1re 7970 |
. . . 4
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3 | 2, 2 | addge0i 8460 |
. . 3
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4 | 1, 1, 3 | mp2an 426 |
. 2
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5 | df-2 8992 |
. 2
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6 | 4, 5 | breqtrri 4042 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 4015 (class class class)co 5888
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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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-setind 4548 ax-cnex 7916 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-icn 7920 ax-addcl 7921 ax-addrcl 7922 ax-mulcl 7923 ax-addcom 7925 ax-addass 7927 ax-i2m1 7930 ax-0lt1 7931 ax-0id 7933 ax-rnegex 7934 ax-pre-ltirr 7937 ax-pre-ltwlin 7938 ax-pre-lttrn 7939 ax-pre-ltadd 7941 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-nel 2453 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-xp 4644 df-cnv 4646 df-iota 5190 df-fv 5236 df-ov 5891 df-pnf 8008 df-mnf 8009 df-xr 8010 df-ltxr 8011 df-le 8012 df-2 8992 |
This theorem is referenced by: expubnd 10591 4bc2eq6 10768 sqrt4 11070 sqrt2gt1lt2 11072 amgm2 11141 bdtrilem 11261 ege2le3 11693 cos2bnd 11782 evennn2n 11902 6gcd4e2 12010 sqrt2irrlem 12175 sqrt2irraplemnn 12193 oddennn 12407 sincos4thpi 14614 lgslem1 14754 m1lgs 14805 |
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