Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemg27b | Structured version Visualization version Unicode version |
Description: TODO: Fix comment. (Contributed by NM, 28-May-2013.) |
Ref | Expression |
---|---|
cdlemg12.l | |
cdlemg12.j | |
cdlemg12.m | |
cdlemg12.a | |
cdlemg12.h | |
cdlemg12.t | |
cdlemg12b.r | |
cdlemg31.n |
Ref | Expression |
---|---|
cdlemg27b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp11 1091 | . . . . 5 | |
2 | simp12 1092 | . . . . 5 | |
3 | simp13 1093 | . . . . 5 | |
4 | simp22 1095 | . . . . 5 | |
5 | simp23l 1182 | . . . . 5 | |
6 | simp31 1097 | . . . . 5 | |
7 | cdlemg12.l | . . . . . 6 | |
8 | cdlemg12.j | . . . . . 6 | |
9 | cdlemg12.m | . . . . . 6 | |
10 | cdlemg12.a | . . . . . 6 | |
11 | cdlemg12.h | . . . . . 6 | |
12 | cdlemg12.t | . . . . . 6 | |
13 | cdlemg12b.r | . . . . . 6 | |
14 | cdlemg31.n | . . . . . 6 | |
15 | 7, 8, 9, 10, 11, 12, 13, 14 | cdlemg31b0a 35983 | . . . . 5 |
16 | 1, 2, 3, 4, 5, 6, 15 | syl132anc 1344 | . . . 4 |
17 | simp23r 1183 | . . . . . 6 | |
18 | 17 | adantr 481 | . . . . 5 |
19 | simp11l 1172 | . . . . . . . . . 10 | |
20 | 19 | adantr 481 | . . . . . . . . 9 |
21 | hlatl 34647 | . . . . . . . . 9 | |
22 | 20, 21 | syl 17 | . . . . . . . 8 |
23 | simpl21 1139 | . . . . . . . 8 | |
24 | simpr 477 | . . . . . . . 8 | |
25 | 7, 10 | atcmp 34598 | . . . . . . . 8 |
26 | 22, 23, 24, 25 | syl3anc 1326 | . . . . . . 7 |
27 | 26 | necon3bbid 2831 | . . . . . 6 |
28 | 19 | adantr 481 | . . . . . . . . . 10 |
29 | 28, 21 | syl 17 | . . . . . . . . 9 |
30 | simpl21 1139 | . . . . . . . . 9 | |
31 | eqid 2622 | . . . . . . . . . 10 | |
32 | 7, 31, 10 | atnle0 34596 | . . . . . . . . 9 |
33 | 29, 30, 32 | syl2anc 693 | . . . . . . . 8 |
34 | simpr 477 | . . . . . . . . 9 | |
35 | 34 | breq2d 4665 | . . . . . . . 8 |
36 | 33, 35 | mtbird 315 | . . . . . . 7 |
37 | 17 | adantr 481 | . . . . . . 7 |
38 | 36, 37 | 2thd 255 | . . . . . 6 |
39 | 27, 38 | jaodan 826 | . . . . 5 |
40 | 18, 39 | mpbird 247 | . . . 4 |
41 | 16, 40 | mpdan 702 | . . 3 |
42 | simp32 1098 | . . . 4 | |
43 | hllat 34650 | . . . . . . . 8 | |
44 | 19, 43 | syl 17 | . . . . . . 7 |
45 | simp21 1094 | . . . . . . . 8 | |
46 | eqid 2622 | . . . . . . . . 9 | |
47 | 46, 10 | atbase 34576 | . . . . . . . 8 |
48 | 45, 47 | syl 17 | . . . . . . 7 |
49 | simp12l 1174 | . . . . . . . 8 | |
50 | simp22l 1180 | . . . . . . . 8 | |
51 | 46, 8, 10 | hlatjcl 34653 | . . . . . . . 8 |
52 | 19, 49, 50, 51 | syl3anc 1326 | . . . . . . 7 |
53 | simp13l 1176 | . . . . . . . 8 | |
54 | simp33 1099 | . . . . . . . . 9 | |
55 | 7, 10, 11, 12, 13 | trlat 35456 | . . . . . . . . 9 |
56 | 1, 2, 5, 54, 55 | syl112anc 1330 | . . . . . . . 8 |
57 | 46, 8, 10 | hlatjcl 34653 | . . . . . . . 8 |
58 | 19, 53, 56, 57 | syl3anc 1326 | . . . . . . 7 |
59 | 46, 7, 9 | latlem12 17078 | . . . . . . 7 |
60 | 44, 48, 52, 58, 59 | syl13anc 1328 | . . . . . 6 |
61 | 14 | breq2i 4661 | . . . . . 6 |
62 | 60, 61 | syl6bbr 278 | . . . . 5 |
63 | 62 | biimpd 219 | . . . 4 |
64 | 42, 63 | mpand 711 | . . 3 |
65 | 41, 64 | mtod 189 | . 2 |
66 | 7, 11, 12, 13 | trlle 35471 | . . . . 5 |
67 | 1, 5, 66 | syl2anc 693 | . . . 4 |
68 | simp13r 1177 | . . . 4 | |
69 | nbrne2 4673 | . . . 4 | |
70 | 67, 68, 69 | syl2anc 693 | . . 3 |
71 | 7, 8, 10 | hlatexch1 34681 | . . 3 |
72 | 19, 56, 45, 53, 70, 71 | syl131anc 1339 | . 2 |
73 | 65, 72 | mtod 189 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wo 383 wa 384 w3a 1037 wceq 1483 wcel 1990 wne 2794 class class class wbr 4653 cfv 5888 (class class class)co 6650 cbs 15857 cple 15948 cjn 16944 cmee 16945 cp0 17037 clat 17045 catm 34550 cal 34551 chlt 34637 clh 35270 cltrn 35387 ctrl 35445 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-iin 4523 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-map 7859 df-preset 16928 df-poset 16946 df-plt 16958 df-lub 16974 df-glb 16975 df-join 16976 df-meet 16977 df-p0 17039 df-p1 17040 df-lat 17046 df-clat 17108 df-oposet 34463 df-ol 34465 df-oml 34466 df-covers 34553 df-ats 34554 df-atl 34585 df-cvlat 34609 df-hlat 34638 df-llines 34784 df-psubsp 34789 df-pmap 34790 df-padd 35082 df-lhyp 35274 df-laut 35275 df-ldil 35390 df-ltrn 35391 df-trl 35446 |
This theorem is referenced by: cdlemg28b 35991 |
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