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 7800 | . . . . 5 | |
2 | 1 | 3coml 1173 | . . . 4 |
3 | orcom 702 | . . . 4 | |
4 | 2, 3 | syl6ib 160 | . . 3 |
5 | 4 | con3d 605 | . 2 |
6 | lenlt 7808 | . . . . 5 | |
7 | 6 | 3adant3 986 | . . . 4 |
8 | lenlt 7808 | . . . . 5 | |
9 | 8 | 3adant1 984 | . . . 4 |
10 | 7, 9 | anbi12d 464 | . . 3 |
11 | ioran 726 | . . 3 | |
12 | 10, 11 | syl6bbr 197 | . 2 |
13 | lenlt 7808 | . . 3 | |
14 | 13 | 3adant2 985 | . 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 682 w3a 947 wcel 1465 class class class wbr 3899 cr 7587 clt 7768 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: letri 7839 letrd 7854 le2add 8174 le2sub 8191 p1le 8575 lemul12b 8587 lemul12a 8588 zletr 9071 peano2uz2 9126 ledivge1le 9481 fznlem 9789 elfz1b 9838 elfz0fzfz0 9871 fz0fzelfz0 9872 fz0fzdiffz0 9875 elfzmlbp 9877 difelfznle 9880 ssfzo12bi 9970 flqge 10023 fldiv4p1lem1div2 10046 monoord 10217 leexp2r 10315 expubnd 10318 le2sq2 10336 facwordi 10454 faclbnd3 10457 facavg 10460 fimaxre2 10966 fsumabs 11202 cvgratnnlemnexp 11261 cvgratnnlemmn 11262 algcvga 11659 prmdvdsfz 11746 prmfac1 11757 sincosq1lem 12833 |
Copyright terms: Public domain | W3C validator |