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Mirrors > Home > ILE Home > Th. List > lenlt | Unicode version |
Description: 'Less than or equal to' expressed in terms of 'less than'. Part of definition 11.2.7(vi) of [HoTT], p. (varies). (Contributed by NM, 13-May-1999.) |
Ref | Expression |
---|---|
lenlt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexr 7938 | . 2 | |
2 | rexr 7938 | . 2 | |
3 | xrlenlt 7957 | . 2 | |
4 | 1, 2, 3 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 2135 class class class wbr 3979 cr 7746 cxr 7926 clt 7927 cle 7928 |
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-14 2138 ax-ext 2146 ax-sep 4097 ax-pow 4150 ax-pr 4184 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 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-ral 2447 df-rex 2448 df-v 2726 df-dif 3116 df-un 3118 df-in 3120 df-ss 3127 df-pw 3558 df-sn 3579 df-pr 3580 df-op 3582 df-br 3980 df-opab 4041 df-xp 4607 df-cnv 4609 df-xr 7931 df-le 7933 |
This theorem is referenced by: letri3 7973 ltleletr 7974 letr 7975 leid 7976 eqlelt 7979 ltle 7980 lelttr 7981 ltletr 7982 lenlti 7993 lenltd 8010 lemul1 8485 msqge0 8508 mulge0 8511 ltleap 8524 recgt0 8739 lediv1 8758 dfinfre 8845 nnge1 8874 nnnlt1 8877 avgle1 9091 avgle2 9092 nn0nlt0 9134 zltnle 9231 zleloe 9232 zdcle 9261 recnz 9278 btwnnz 9279 prime 9284 fznlem 9970 fzonlt0 10096 qltnle 10175 bcval4 10659 resqrexlemgt0 10956 climge0 11260 infpnlem1 12283 efle 13295 logleb 13394 cxple 13435 cxple3 13439 supfz 13840 inffz 13841 |
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