Step |
Hyp |
Ref |
Expression |
1 |
|
hdmap14lem1a.h |
|
2 |
|
hdmap14lem1a.u |
|
3 |
|
hdmap14lem1a.v |
|
4 |
|
hdmap14lem1a.t |
|
5 |
|
hdmap14lem1a.r |
|
6 |
|
hdmap14lem1a.b |
|
7 |
|
hdmap14lem1a.c |
|
8 |
|
hdmap14lem2a.e |
|
9 |
|
hdmap14lem1a.l |
|
10 |
|
hdmap14lem2a.p |
|
11 |
|
hdmap14lem2a.a |
|
12 |
|
hdmap14lem1a.s |
|
13 |
|
hdmap14lem1a.k |
|
14 |
|
hdmap14lem3a.x |
|
15 |
|
hdmap14lem1a.f |
|
16 |
|
fvoveq1 |
|
17 |
16
|
eqeq1d |
|
18 |
17
|
rexbidv |
|
19 |
|
difss |
|
20 |
13
|
adantr |
|
21 |
14
|
adantr |
|
22 |
15
|
adantr |
|
23 |
|
eqid |
|
24 |
|
simpr |
|
25 |
1 2 3 4 5 6 7 8 9 10 11 12 20 21 22 23 24
|
hdmap14lem1a |
|
26 |
25
|
eqcomd |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
1 7 13
|
lcdlvec |
|
30 |
1 2 13
|
dvhlmod |
|
31 |
3 5 4 6
|
lmodvscl |
|
32 |
30 15 14 31
|
syl3anc |
|
33 |
1 2 3 7 27 12 13 32
|
hdmapcl |
|
34 |
1 2 3 7 27 12 13 14
|
hdmapcl |
|
35 |
27 10 11 28 8 9 29 33 34
|
lspsneq |
|
36 |
35
|
adantr |
|
37 |
26 36
|
mpbid |
|
38 |
|
ssrexv |
|
39 |
19 37 38
|
mpsyl |
|
40 |
1 7 13
|
lcdlmod |
|
41 |
10 11 28
|
lmod0cl |
|
42 |
40 41
|
syl |
|
43 |
|
eqid |
|
44 |
|
eqid |
|
45 |
1 2 43 7 44 12 13
|
hdmapval0 |
|
46 |
3 5 4 23 43
|
lmod0vs |
|
47 |
30 14 46
|
syl2anc |
|
48 |
47
|
fveq2d |
|
49 |
27 10 8 28 44
|
lmod0vs |
|
50 |
40 34 49
|
syl2anc |
|
51 |
45 48 50
|
3eqtr4d |
|
52 |
|
oveq1 |
|
53 |
52
|
rspceeqv |
|
54 |
42 51 53
|
syl2anc |
|
55 |
18 39 54
|
pm2.61ne |
|