![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > lttrd | Unicode version |
Description: Transitive law deduction for 'less than'. (Contributed by NM, 9-Jan-2006.) |
Ref | Expression |
---|---|
ltd.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
ltd.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
letrd.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
lttrd.4 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
lttrd.5 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
lttrd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lttrd.4 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | lttrd.5 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | ltd.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | ltd.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | letrd.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | lttr 7862 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 3, 4, 5, 6 | syl3anc 1217 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 1, 2, 7 | mp2and 430 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-pre-lttrn 7758 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-pnf 7826 df-mnf 7827 df-ltxr 7829 |
This theorem is referenced by: exbtwnzlemex 10058 rebtwn2z 10063 qbtwnrelemcalc 10064 expgt1 10362 ltexp2a 10376 expnlbnd2 10448 expcanlem 10493 expcan 10494 cvg1nlemcxze 10786 cvg1nlemcau 10788 cvg1nlemres 10789 recvguniqlem 10798 resqrexlemdecn 10816 resqrexlemcvg 10823 resqrexlemga 10827 qdenre 11006 reccn2ap 11114 georeclim 11314 geoisumr 11319 cvgratz 11333 efcllemp 11401 efgt1 11440 cos12dec 11510 dvdslelemd 11577 ivthinclemlr 12823 ivthinclemur 12825 limcimolemlt 12841 reeff1olem 12900 sin0pilem1 12910 pilem3 12912 coseq0negpitopi 12965 tangtx 12967 cos02pilt1 12980 rplogcl 13008 cxplt 13044 cxple 13045 cvgcmp2nlemabs 13402 trilpolemlt1 13409 apdifflemf 13414 |
Copyright terms: Public domain | W3C validator |