Step |
Hyp |
Ref |
Expression |
1 |
|
rmodislmod.v |
|
2 |
|
rmodislmod.a |
|
3 |
|
rmodislmod.s |
|
4 |
|
rmodislmod.f |
|
5 |
|
rmodislmod.k |
|
6 |
|
rmodislmod.p |
|
7 |
|
rmodislmod.t |
|
8 |
|
rmodislmod.u |
|
9 |
|
rmodislmod.r |
|
10 |
|
rmodislmod.m |
|
11 |
|
rmodislmod.l |
|
12 |
|
simprl |
|
13 |
12
|
2ralimi |
|
14 |
13
|
2ralimi |
|
15 |
|
ralrot3 |
|
16 |
1
|
grpbn0 |
|
17 |
16
|
3ad2ant1 |
|
18 |
9 17
|
ax-mp |
|
19 |
|
rspn0 |
|
20 |
18 19
|
ax-mp |
|
21 |
|
oveq1 |
|
22 |
21
|
oveq2d |
|
23 |
|
oveq2 |
|
24 |
23
|
oveq1d |
|
25 |
22 24
|
eqeq12d |
|
26 |
|
oveq2 |
|
27 |
26
|
oveq2d |
|
28 |
|
oveq2 |
|
29 |
27 28
|
eqeq12d |
|
30 |
|
oveq1 |
|
31 |
|
oveq1 |
|
32 |
31
|
oveq1d |
|
33 |
30 32
|
eqeq12d |
|
34 |
25 29 33
|
rspc3v |
|
35 |
34
|
3com12 |
|
36 |
20 35
|
syl5com |
|
37 |
15 36
|
sylbi |
|
38 |
|
eqcom |
|
39 |
37 38
|
syl6ibr |
|
40 |
14 39
|
syl |
|
41 |
40
|
3ad2ant3 |
|
42 |
9 41
|
ax-mp |
|
43 |
42
|
adantl |
|
44 |
5 7
|
crngcom |
|
45 |
44
|
3expb |
|
46 |
45
|
expcom |
|
47 |
46
|
ancoms |
|
48 |
47
|
3adant3 |
|
49 |
48
|
impcom |
|
50 |
49
|
oveq2d |
|
51 |
43 50
|
eqtrd |
|
52 |
10
|
a1i |
|
53 |
|
oveq12 |
|
54 |
53
|
ancoms |
|
55 |
54
|
adantl |
|
56 |
|
simp2 |
|
57 |
|
simp3 |
|
58 |
|
ovexd |
|
59 |
52 55 56 57 58
|
ovmpod |
|
60 |
59
|
oveq2d |
|
61 |
|
oveq12 |
|
62 |
61
|
ancoms |
|
63 |
62
|
adantl |
|
64 |
|
simp1 |
|
65 |
|
simpl1 |
|
66 |
65
|
2ralimi |
|
67 |
66
|
2ralimi |
|
68 |
|
ringgrp |
|
69 |
5
|
grpbn0 |
|
70 |
68 69
|
syl |
|
71 |
70
|
3ad2ant2 |
|
72 |
9 71
|
ax-mp |
|
73 |
|
rspn0 |
|
74 |
72 73
|
ax-mp |
|
75 |
|
ralcom |
|
76 |
|
rspn0 |
|
77 |
18 76
|
ax-mp |
|
78 |
|
oveq2 |
|
79 |
78
|
eleq1d |
|
80 |
31
|
eleq1d |
|
81 |
79 80
|
rspc2v |
|
82 |
77 81
|
syl5com |
|
83 |
75 82
|
sylbi |
|
84 |
67 74 83
|
3syl |
|
85 |
84
|
3ad2ant3 |
|
86 |
9 85
|
ax-mp |
|
87 |
86
|
3adant1 |
|
88 |
|
ovexd |
|
89 |
52 63 64 87 88
|
ovmpod |
|
90 |
60 89
|
eqtrd |
|
91 |
90
|
adantl |
|
92 |
|
oveq12 |
|
93 |
92
|
ancoms |
|
94 |
93
|
adantl |
|
95 |
5 7
|
ringcl |
|
96 |
95
|
3expib |
|
97 |
96
|
3ad2ant2 |
|
98 |
9 97
|
ax-mp |
|
99 |
98
|
3adant3 |
|
100 |
|
ovexd |
|
101 |
52 94 99 57 100
|
ovmpod |
|
102 |
101
|
adantl |
|
103 |
51 91 102
|
3eqtr4rd |
|