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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 7071 | . 2 | |
2 | rexr 7071 | . 2 | |
3 | xrlenlt 7084 | . 2 | |
4 | 1, 2, 3 | syl2an 273 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wcel 1393 class class class wbr 3764 cr 6888 cxr 7059 clt 7060 cle 7061 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-xr 7064 df-le 7066 |
This theorem is referenced by: letri3 7099 ltleletr 7100 letr 7101 leid 7102 ltle 7105 lelttr 7106 ltletr 7107 lenlti 7118 lenltd 7134 lemul1 7584 msqge0 7607 mulge0 7610 ltleap 7621 recgt0 7816 lediv1 7835 nnge1 7937 nnnlt1 7940 avgle1 8165 avgle2 8166 nn0nlt0 8208 zltnle 8291 zleloe 8292 zdcle 8317 recnz 8333 btwnnz 8334 prime 8337 fznlem 8905 fzonlt0 9023 qltnle 9101 resqrexlemgt0 9618 climge0 9845 |
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