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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 7779 | . 2 | |
2 | rexr 7779 | . 2 | |
3 | xrlenlt 7797 | . 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 1465 class class class wbr 3899 cr 7587 cxr 7767 clt 7768 cle 7769 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-xr 7772 df-le 7774 |
This theorem is referenced by: letri3 7813 ltleletr 7814 letr 7815 leid 7816 ltle 7819 lelttr 7820 ltletr 7821 lenlti 7832 lenltd 7848 lemul1 8323 msqge0 8346 mulge0 8349 ltleap 8362 recgt0 8576 lediv1 8595 dfinfre 8682 nnge1 8711 nnnlt1 8714 avgle1 8928 avgle2 8929 nn0nlt0 8971 zltnle 9068 zleloe 9069 zdcle 9095 recnz 9112 btwnnz 9113 prime 9118 fznlem 9789 fzonlt0 9912 qltnle 9991 bcval4 10466 resqrexlemgt0 10760 climge0 11062 efler 11332 supfz 13164 inffz 13165 |
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