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Mirrors > Home > ILE Home > Th. List > 0le1 | Unicode version |
Description: 0 is less than or equal to 1. (Contributed by Mario Carneiro, 29-Apr-2015.) |
Ref | Expression |
---|---|
0le1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 7119 | . 2 | |
2 | 1re 7118 | . 2 | |
3 | 0lt1 7236 | . 2 | |
4 | 1, 2, 3 | ltleii 7213 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3785 cc0 6981 c1 6982 cle 7154 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-setind 4280 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-0lt1 7082 ax-rnegex 7085 ax-pre-ltirr 7088 ax-pre-lttrn 7090 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-nel 2340 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-pnf 7155 df-mnf 7156 df-xr 7157 df-ltxr 7158 df-le 7159 |
This theorem is referenced by: lemulge11 7944 0le2 8129 1eluzge0 8662 0elunit 9008 1elunit 9009 fldiv4p1lem1div2 9307 q1mod 9358 expge0 9512 expge1 9513 faclbnd3 9670 sqrt1 9932 sqrt2gt1lt2 9935 abs1 9958 nn0oddm1d2 10309 flodddiv4 10334 sqnprm 10517 sqrt2irrap 10558 |
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