![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 7594 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | rexr 7594 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | xrlenlt 7612 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | syl2an 284 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-opab 3906 df-xp 4458 df-cnv 4460 df-xr 7587 df-le 7589 |
This theorem is referenced by: letri3 7627 ltleletr 7628 letr 7629 leid 7630 ltle 7633 lelttr 7634 ltletr 7635 lenlti 7646 lenltd 7662 lemul1 8131 msqge0 8154 mulge0 8157 ltleap 8168 recgt0 8372 lediv1 8391 dfinfre 8478 nnge1 8506 nnnlt1 8509 avgle1 8717 avgle2 8718 nn0nlt0 8760 zltnle 8857 zleloe 8858 zdcle 8884 recnz 8900 btwnnz 8901 prime 8906 fznlem 9516 fzonlt0 9639 qltnle 9718 bcval4 10221 resqrexlemgt0 10514 climge0 10774 efler 11050 supfz 12188 inffz 12189 |
Copyright terms: Public domain | W3C validator |