Step |
Hyp |
Ref |
Expression |
1 |
|
hdmaprnlem1.h |
|
2 |
|
hdmaprnlem1.u |
|
3 |
|
hdmaprnlem1.v |
|
4 |
|
hdmaprnlem1.n |
|
5 |
|
hdmaprnlem1.c |
|
6 |
|
hdmaprnlem1.l |
|
7 |
|
hdmaprnlem1.m |
|
8 |
|
hdmaprnlem1.s |
|
9 |
|
hdmaprnlem1.k |
|
10 |
|
hdmaprnlem1.se |
|
11 |
|
hdmaprnlem1.ve |
|
12 |
|
hdmaprnlem1.e |
|
13 |
|
hdmaprnlem1.ue |
|
14 |
|
hdmaprnlem1.un |
|
15 |
|
hdmaprnlem1.d |
|
16 |
|
hdmaprnlem1.q |
|
17 |
|
hdmaprnlem1.o |
|
18 |
|
hdmaprnlem1.a |
|
19 |
|
hdmaprnlem3e.p |
|
20 |
|
eqid |
|
21 |
1 2 9
|
dvhlvec |
|
22 |
|
eqid |
|
23 |
1 5 9
|
lcdlmod |
|
24 |
1 2 3 5 15 8 9 13
|
hdmapcl |
|
25 |
10
|
eldifad |
|
26 |
15 18
|
lmodvacl |
|
27 |
23 24 25 26
|
syl3anc |
|
28 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14
|
hdmaprnlem1N |
|
29 |
15 18 16 6 23 24 25 28
|
lmodindp1 |
|
30 |
|
eldifsn |
|
31 |
27 29 30
|
sylanbrc |
|
32 |
15 6 16 22 23 31
|
lsatlspsn |
|
33 |
1 7 2 20 5 22 9 32
|
mapdcnvatN |
|
34 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
|
hdmaprnlem3uN |
|
35 |
34
|
necomd |
|
36 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
|
hdmaprnlem3N |
|
37 |
36
|
necomd |
|
38 |
|
eqid |
|
39 |
|
eqid |
|
40 |
1 2 9
|
dvhlmod |
|
41 |
3 39 4
|
lspsncl |
|
42 |
40 13 41
|
syl2anc |
|
43 |
1 7 2 39 5 38 9 42
|
mapdcl2 |
|
44 |
3 39 4
|
lspsncl |
|
45 |
40 11 44
|
syl2anc |
|
46 |
1 7 2 39 5 38 9 45
|
mapdcl2 |
|
47 |
|
eqid |
|
48 |
38 47
|
lsmcl |
|
49 |
23 43 46 48
|
syl3anc |
|
50 |
38
|
lsssssubg |
|
51 |
23 50
|
syl |
|
52 |
51 43
|
sseldd |
|
53 |
51 46
|
sseldd |
|
54 |
15 6
|
lspsnid |
|
55 |
23 24 54
|
syl2anc |
|
56 |
1 2 3 4 5 6 7 8 9 13
|
hdmap10 |
|
57 |
55 56
|
eleqtrrd |
|
58 |
|
eqimss2 |
|
59 |
12 58
|
syl |
|
60 |
15 38 6 23 46 25
|
lspsnel5 |
|
61 |
59 60
|
mpbird |
|
62 |
18 47
|
lsmelvali |
|
63 |
52 53 57 61 62
|
syl22anc |
|
64 |
38 6 23 49 63
|
lspsnel5a |
|
65 |
|
eqid |
|
66 |
1 7 2 39 65 5 47 9 42 45
|
mapdlsm |
|
67 |
64 66
|
sseqtrrd |
|
68 |
15 38 6
|
lspsncl |
|
69 |
23 27 68
|
syl2anc |
|
70 |
1 7 5 38 9
|
mapdrn2 |
|
71 |
69 70
|
eleqtrrd |
|
72 |
39 65
|
lsmcl |
|
73 |
40 42 45 72
|
syl3anc |
|
74 |
1 7 2 39 9 73
|
mapdcl |
|
75 |
1 7 9 71 74
|
mapdcnvordN |
|
76 |
67 75
|
mpbird |
|
77 |
3 4 65 40 13 11
|
lsmpr |
|
78 |
1 7 2 39 9 73
|
mapdcnvid1N |
|
79 |
77 78
|
eqtr4d |
|
80 |
76 79
|
sseqtrrd |
|
81 |
3 19 17 4 20 21 33 13 11 35 37 80
|
lsatfixedN |
|
82 |
|
simpr |
|
83 |
9
|
ad2antrr |
|
84 |
40
|
ad2antrr |
|
85 |
13
|
ad2antrr |
|
86 |
10
|
ad2antrr |
|
87 |
11
|
ad2antrr |
|
88 |
12
|
ad2antrr |
|
89 |
14
|
ad2antrr |
|
90 |
|
simplr |
|
91 |
1 2 3 4 5 6 7 8 83 86 87 88 85 89 15 16 17 18 90
|
hdmaprnlem4tN |
|
92 |
3 19
|
lmodvacl |
|
93 |
84 85 91 92
|
syl3anc |
|
94 |
3 39 4
|
lspsncl |
|
95 |
84 93 94
|
syl2anc |
|
96 |
1 7 2 39 83 95
|
mapdcnvid1N |
|
97 |
82 96
|
eqtr4d |
|
98 |
71
|
ad2antrr |
|
99 |
1 7 2 39 83 95
|
mapdcl |
|
100 |
1 7 83 98 99
|
mapdcnv11N |
|
101 |
97 100
|
mpbid |
|
102 |
101
|
ex |
|
103 |
102
|
reximdva |
|
104 |
81 103
|
mpd |
|