Step |
Hyp |
Ref |
Expression |
1 |
|
lincvalsc0.b |
|
2 |
|
lincvalsc0.s |
|
3 |
|
lincvalsc0.0 |
|
4 |
|
lincvalsc0.z |
|
5 |
|
lincvalsc0.f |
|
6 |
|
simpl |
|
7 |
2
|
eqcomi |
|
8 |
7
|
fveq2i |
|
9 |
2 8 3
|
lmod0cl |
|
10 |
9
|
adantr |
|
11 |
10
|
adantr |
|
12 |
11 5
|
fmptd |
|
13 |
|
fvexd |
|
14 |
|
elmapg |
|
15 |
13 14
|
sylan |
|
16 |
12 15
|
mpbird |
|
17 |
1
|
pweqi |
|
18 |
17
|
eleq2i |
|
19 |
18
|
biimpi |
|
20 |
19
|
adantl |
|
21 |
|
lincval |
|
22 |
6 16 20 21
|
syl3anc |
|
23 |
|
simpr |
|
24 |
3
|
fvexi |
|
25 |
|
eqidd |
|
26 |
25 5
|
fvmptg |
|
27 |
23 24 26
|
sylancl |
|
28 |
27
|
oveq1d |
|
29 |
6
|
adantr |
|
30 |
|
elelpwi |
|
31 |
30
|
expcom |
|
32 |
31
|
adantl |
|
33 |
32
|
imp |
|
34 |
|
eqid |
|
35 |
1 2 34 3 4
|
lmod0vs |
|
36 |
29 33 35
|
syl2anc |
|
37 |
28 36
|
eqtrd |
|
38 |
37
|
mpteq2dva |
|
39 |
38
|
oveq2d |
|
40 |
|
lmodgrp |
|
41 |
40
|
grpmndd |
|
42 |
4
|
gsumz |
|
43 |
41 42
|
sylan |
|
44 |
22 39 43
|
3eqtrd |
|