![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > lttri | Unicode version |
Description: 'Less than' is transitive. Theorem I.17 of [Apostol] p. 20. (Contributed by NM, 14-May-1999.) |
Ref | Expression |
---|---|
lt.1 |
![]() ![]() ![]() ![]() |
lt.2 |
![]() ![]() ![]() ![]() |
lt.3 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
lttri |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | lt.2 |
. 2
![]() ![]() ![]() ![]() | |
3 | lt.3 |
. 2
![]() ![]() ![]() ![]() | |
4 | lttr 8018 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | mp3an 1337 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-un 4430 ax-setind 4533 ax-cnex 7890 ax-resscn 7891 ax-pre-lttrn 7913 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-xp 4629 df-pnf 7981 df-mnf 7982 df-ltxr 7984 |
This theorem is referenced by: 1lt3 9076 2lt4 9078 1lt4 9079 3lt5 9081 2lt5 9082 1lt5 9083 4lt6 9085 3lt6 9086 2lt6 9087 1lt6 9088 5lt7 9090 4lt7 9091 3lt7 9092 2lt7 9093 1lt7 9094 6lt8 9096 5lt8 9097 4lt8 9098 3lt8 9099 2lt8 9100 1lt8 9101 7lt9 9103 6lt9 9104 5lt9 9105 4lt9 9106 3lt9 9107 2lt9 9108 1lt9 9109 8lt10 9501 7lt10 9502 6lt10 9503 5lt10 9504 4lt10 9505 3lt10 9506 2lt10 9507 1lt10 9508 sincos2sgn 11754 cos12dec 11756 epos 11769 ene1 11773 eap1 11774 reeff1o 13858 pipos 13873 pigt3 13929 apdiff 14449 |
Copyright terms: Public domain | W3C validator |