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Mirrors > Home > ILE Home > Th. List > 0le0 | GIF version |
Description: Zero is nonnegative. (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
0le0 | ⊢ 0 ≤ 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 7909 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | leidi 8393 | 1 ⊢ 0 ≤ 0 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3987 0cc0 7763 ≤ cle 7944 |
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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 ax-setind 4519 ax-cnex 7854 ax-resscn 7855 ax-1re 7857 ax-addrcl 7860 ax-rnegex 7872 ax-pre-ltirr 7875 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 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-ne 2341 df-nel 2436 df-ral 2453 df-rex 2454 df-rab 2457 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-uni 3795 df-br 3988 df-opab 4049 df-xp 4615 df-cnv 4617 df-pnf 7945 df-mnf 7946 df-xr 7947 df-ltxr 7948 df-le 7949 |
This theorem is referenced by: nn0ge0 9149 nn0ledivnn 9713 xsubge0 9827 0e0icopnf 9925 0e0iccpnf 9926 0elunit 9932 q0mod 10300 exp0 10469 sqrt0rlem 10956 sqrt00 10993 xrmaxadd 11213 fsumabs 11417 pcmptdvds 12286 trilpolemclim 14030 trilpolemlt1 14035 nconstwlpolemgt0 14057 |
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