Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > letri | Unicode version |
Description: 'Less than or equal to' is transitive. (Contributed by NM, 14-May-1999.) |
Ref | Expression |
---|---|
lt.1 | |
lt.2 | |
lt.3 |
Ref | Expression |
---|---|
letri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 | . 2 | |
2 | lt.2 | . 2 | |
3 | lt.3 | . 2 | |
4 | letr 7815 | . 2 | |
5 | 1, 2, 3, 4 | mp3an 1300 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 class class class wbr 3899 cr 7587 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-13 1476 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 ax-un 4325 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 ax-pre-ltwlin 7701 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 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-ne 2286 df-nel 2381 df-ral 2398 df-rex 2399 df-rab 2402 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-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-pnf 7770 df-mnf 7771 df-xr 7772 df-ltxr 7773 df-le 7774 |
This theorem is referenced by: le2tri3i 7840 nn0lele2xi 8996 strleun 11975 |
Copyright terms: Public domain | W3C validator |