Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > letr | Unicode version |
Description: Transitive law. (Contributed by NM, 12-Nov-1999.) |
Ref | Expression |
---|---|
letr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axltwlin 7825 | . . . . 5 | |
2 | 1 | 3coml 1188 | . . . 4 |
3 | orcom 717 | . . . 4 | |
4 | 2, 3 | syl6ib 160 | . . 3 |
5 | 4 | con3d 620 | . 2 |
6 | lenlt 7833 | . . . . 5 | |
7 | 6 | 3adant3 1001 | . . . 4 |
8 | lenlt 7833 | . . . . 5 | |
9 | 8 | 3adant1 999 | . . . 4 |
10 | 7, 9 | anbi12d 464 | . . 3 |
11 | ioran 741 | . . 3 | |
12 | 10, 11 | syl6bbr 197 | . 2 |
13 | lenlt 7833 | . . 3 | |
14 | 13 | 3adant2 1000 | . 2 |
15 | 5, 12, 14 | 3imtr4d 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 697 w3a 962 wcel 1480 class class class wbr 3924 cr 7612 clt 7793 cle 7794 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 ax-pre-ltwlin 7726 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-nel 2402 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-xp 4540 df-cnv 4542 df-pnf 7795 df-mnf 7796 df-xr 7797 df-ltxr 7798 df-le 7799 |
This theorem is referenced by: letri 7864 letrd 7879 le2add 8199 le2sub 8216 p1le 8600 lemul12b 8612 lemul12a 8613 zletr 9096 peano2uz2 9151 ledivge1le 9506 fznlem 9814 elfz1b 9863 elfz0fzfz0 9896 fz0fzelfz0 9897 fz0fzdiffz0 9900 elfzmlbp 9902 difelfznle 9905 ssfzo12bi 9995 flqge 10048 fldiv4p1lem1div2 10071 monoord 10242 leexp2r 10340 expubnd 10343 le2sq2 10361 facwordi 10479 faclbnd3 10482 facavg 10485 fimaxre2 10991 fsumabs 11227 cvgratnnlemnexp 11286 cvgratnnlemmn 11287 algcvga 11721 prmdvdsfz 11808 prmfac1 11819 sincosq1lem 12895 |
Copyright terms: Public domain | W3C validator |