Step |
Hyp |
Ref |
Expression |
1 |
|
lincscmcl.s |
|
2 |
|
lincscmcl.r |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
3 4 2
|
lcoval |
|
6 |
5
|
adantr |
|
7 |
|
simpl |
|
8 |
7
|
ad2antrr |
|
9 |
|
simpr |
|
10 |
9
|
adantr |
|
11 |
|
simprl |
|
12 |
3 4 1 2
|
lmodvscl |
|
13 |
8 10 11 12
|
syl3anc |
|
14 |
4
|
lmodring |
|
15 |
14
|
ad2antrr |
|
16 |
15
|
adantl |
|
17 |
16
|
adantr |
|
18 |
9
|
adantl |
|
19 |
18
|
adantr |
|
20 |
|
elmapi |
|
21 |
|
ffvelrn |
|
22 |
21
|
ex |
|
23 |
20 22
|
syl |
|
24 |
23
|
adantr |
|
25 |
24
|
ad2antrr |
|
26 |
25
|
imp |
|
27 |
|
eqid |
|
28 |
2 27
|
ringcl |
|
29 |
17 19 26 28
|
syl3anc |
|
30 |
29
|
fmpttd |
|
31 |
2
|
fvexi |
|
32 |
|
simpr |
|
33 |
32
|
adantr |
|
34 |
33
|
adantl |
|
35 |
|
elmapg |
|
36 |
31 34 35
|
sylancr |
|
37 |
30 36
|
mpbird |
|
38 |
15 33 9
|
3jca |
|
39 |
38
|
adantl |
|
40 |
|
simpl |
|
41 |
40
|
ad2antrr |
|
42 |
|
simprl |
|
43 |
42
|
ad2antrr |
|
44 |
2
|
rmfsupp |
|
45 |
39 41 43 44
|
syl3anc |
|
46 |
|
oveq2 |
|
47 |
46
|
adantl |
|
48 |
47
|
adantl |
|
49 |
48
|
ad2antrr |
|
50 |
|
simprl |
|
51 |
40
|
adantr |
|
52 |
51 9
|
anim12i |
|
53 |
|
eqid |
|
54 |
|
eqid |
|
55 |
1 27 53 2 54
|
lincscm |
|
56 |
50 52 43 55
|
syl3anc |
|
57 |
49 56
|
eqtrd |
|
58 |
|
breq1 |
|
59 |
|
oveq1 |
|
60 |
59
|
eqeq2d |
|
61 |
58 60
|
anbi12d |
|
62 |
61
|
rspcev |
|
63 |
37 45 57 62
|
syl12anc |
|
64 |
63
|
ex |
|
65 |
64
|
ex |
|
66 |
65
|
rexlimiva |
|
67 |
66
|
impcom |
|
68 |
67
|
impcom |
|
69 |
3 4 2
|
lcoval |
|
70 |
69
|
ad2antrr |
|
71 |
13 68 70
|
mpbir2and |
|
72 |
71
|
ex |
|
73 |
6 72
|
sylbid |
|
74 |
73
|
3impia |
|