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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 7857 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | leidi 8339 | 1 ⊢ 0 ≤ 0 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3961 0cc0 7711 ≤ cle 7892 |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-13 2127 ax-14 2128 ax-ext 2136 ax-sep 4078 ax-pow 4130 ax-pr 4164 ax-un 4388 ax-setind 4490 ax-cnex 7802 ax-resscn 7803 ax-1re 7805 ax-addrcl 7808 ax-rnegex 7820 ax-pre-ltirr 7823 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ne 2325 df-nel 2420 df-ral 2437 df-rex 2438 df-rab 2441 df-v 2711 df-dif 3100 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-br 3962 df-opab 4022 df-xp 4585 df-cnv 4587 df-pnf 7893 df-mnf 7894 df-xr 7895 df-ltxr 7896 df-le 7897 |
This theorem is referenced by: nn0ge0 9094 nn0ledivnn 9652 xsubge0 9763 0e0icopnf 9861 0e0iccpnf 9862 0elunit 9868 q0mod 10232 exp0 10401 sqrt0rlem 10880 sqrt00 10917 xrmaxadd 11135 fsumabs 11339 trilpolemclim 13548 trilpolemlt1 13553 nconstwlpolemgt0 13575 |
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