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Mirrors > Home > ILE Home > Th. List > leidd | Unicode version |
Description: 'Less than or equal to' is reflexive. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
leidd.1 |
Ref | Expression |
---|---|
leidd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leidd.1 | . 2 | |
2 | leid 7973 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 class class class wbr 3976 cr 7743 cle 7925 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-pre-ltirr 7856 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-pnf 7926 df-mnf 7927 df-xr 7928 df-ltxr 7929 df-le 7930 |
This theorem is referenced by: zextle 9273 uzind 9293 uzid 9471 z2ge 9753 nn0fz0 10044 fvinim0ffz 10166 flid 10209 modqabs2 10283 monoord 10401 leexp2r 10499 facwordi 10642 faclbnd6 10646 sqrtgt0 10962 abs00ap 10990 isumlessdc 11423 cvgratnnlemnexp 11451 cvgratnnlemmn 11452 eirraplem 11703 nn0seqcvgd 11952 pcidlem 12231 pc2dvds 12238 pcprmpw2 12241 pcmpt 12250 trilpolemclim 13749 trilpolemisumle 13751 trilpolemeq1 13753 |
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