Step |
Hyp |
Ref |
Expression |
1 |
|
lmod1zr.r |
|
2 |
|
lmod1zr.m |
|
3 |
|
elsni |
|
4 |
|
fveq2 |
|
5 |
4
|
adantl |
|
6 |
|
op2ndg |
|
7 |
6
|
ancoms |
|
8 |
|
snidg |
|
9 |
8
|
adantr |
|
10 |
7 9
|
eqeltrd |
|
11 |
10
|
adantr |
|
12 |
5 11
|
eqeltrd |
|
13 |
3 12
|
sylan2 |
|
14 |
13
|
fmpttd |
|
15 |
|
opex |
|
16 |
|
simpl |
|
17 |
|
fsng |
|
18 |
15 16 17
|
sylancr |
|
19 |
14 18
|
mpbid |
|
20 |
|
xpsng |
|
21 |
20
|
ancoms |
|
22 |
21
|
eqcomd |
|
23 |
22
|
mpteq1d |
|
24 |
19 23
|
eqtr3d |
|
25 |
|
vex |
|
26 |
|
vex |
|
27 |
25 26
|
op2ndd |
|
28 |
27
|
mpompt |
|
29 |
28
|
a1i |
|
30 |
|
snex |
|
31 |
1
|
rngbase |
|
32 |
30 31
|
mp1i |
|
33 |
|
eqidd |
|
34 |
|
mpoeq12 |
|
35 |
32 33 34
|
syl2anc |
|
36 |
24 29 35
|
3eqtrd |
|
37 |
36
|
opeq2d |
|
38 |
37
|
sneqd |
|
39 |
38
|
uneq2d |
|
40 |
2 39
|
eqtrid |
|
41 |
1
|
ring1 |
|
42 |
|
eqidd |
|
43 |
|
id |
|
44 |
42 43
|
cbvmpov |
|
45 |
44
|
opeq2i |
|
46 |
45
|
sneqi |
|
47 |
46
|
uneq2i |
|
48 |
47
|
lmod1 |
|
49 |
41 48
|
sylan2 |
|
50 |
40 49
|
eqeltrd |
|