Step |
Hyp |
Ref |
Expression |
1 |
|
lincsumcl.b |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
2 3 4
|
lcoval |
|
6 |
2 3 4
|
lcoval |
|
7 |
5 6
|
anbi12d |
|
8 |
|
simpll |
|
9 |
|
simpll |
|
10 |
9
|
adantl |
|
11 |
|
simprl |
|
12 |
11
|
adantl |
|
13 |
2 1
|
lmodvacl |
|
14 |
8 10 12 13
|
syl3anc |
|
15 |
3
|
lmodfgrp |
|
16 |
|
grpmnd |
|
17 |
15 16
|
syl |
|
18 |
17
|
adantr |
|
19 |
18
|
adantl |
|
20 |
|
simpr |
|
21 |
20
|
adantl |
|
22 |
|
simpll |
|
23 |
|
simpl |
|
24 |
22 23
|
anim12i |
|
25 |
24
|
adantr |
|
26 |
|
eqid |
|
27 |
4 26
|
ofaddmndmap |
|
28 |
19 21 25 27
|
syl3anc |
|
29 |
17
|
anim1i |
|
30 |
29
|
adantl |
|
31 |
|
simprl |
|
32 |
31
|
adantr |
|
33 |
|
simprl |
|
34 |
32 33
|
anim12i |
|
35 |
34
|
adantr |
|
36 |
4
|
mndpfsupp |
|
37 |
30 25 35 36
|
syl3anc |
|
38 |
|
oveq12 |
|
39 |
38
|
expcom |
|
40 |
39
|
adantl |
|
41 |
40
|
adantl |
|
42 |
41
|
com12 |
|
43 |
42
|
adantl |
|
44 |
43
|
adantl |
|
45 |
44
|
adantr |
|
46 |
45
|
imp |
|
47 |
46
|
adantr |
|
48 |
|
simpr |
|
49 |
|
eqid |
|
50 |
|
eqid |
|
51 |
1 49 50 3 4 26
|
lincsum |
|
52 |
48 25 35 51
|
syl3anc |
|
53 |
47 52
|
eqtrd |
|
54 |
|
breq1 |
|
55 |
|
oveq1 |
|
56 |
55
|
eqeq2d |
|
57 |
54 56
|
anbi12d |
|
58 |
57
|
rspcev |
|
59 |
28 37 53 58
|
syl12anc |
|
60 |
59
|
exp41 |
|
61 |
60
|
rexlimiva |
|
62 |
61
|
expd |
|
63 |
62
|
impcom |
|
64 |
63
|
com13 |
|
65 |
64
|
rexlimiva |
|
66 |
65
|
impcom |
|
67 |
66
|
impcom |
|
68 |
67
|
impcom |
|
69 |
2 3 4
|
lcoval |
|
70 |
69
|
adantr |
|
71 |
14 68 70
|
mpbir2and |
|
72 |
71
|
ex |
|
73 |
7 72
|
sylbid |
|
74 |
73
|
imp |
|