Step |
Hyp |
Ref |
Expression |
1 |
|
mendassa.a |
|
2 |
1
|
mendbas |
|
3 |
2
|
a1i |
|
4 |
|
eqidd |
|
5 |
|
eqidd |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
1 2 6 7
|
mendplusg |
|
9 |
6
|
lmhmplusg |
|
10 |
8 9
|
eqeltrd |
|
11 |
10
|
3adant1 |
|
12 |
|
simpr1 |
|
13 |
|
simpr2 |
|
14 |
12 13 9
|
syl2anc |
|
15 |
|
simpr3 |
|
16 |
1 2 6 7
|
mendplusg |
|
17 |
14 15 16
|
syl2anc |
|
18 |
12 13 8
|
syl2anc |
|
19 |
18
|
oveq1d |
|
20 |
6
|
lmhmplusg |
|
21 |
13 15 20
|
syl2anc |
|
22 |
1 2 6 7
|
mendplusg |
|
23 |
12 21 22
|
syl2anc |
|
24 |
1 2 6 7
|
mendplusg |
|
25 |
13 15 24
|
syl2anc |
|
26 |
25
|
oveq2d |
|
27 |
|
lmodgrp |
|
28 |
|
grpmnd |
|
29 |
27 28
|
syl |
|
30 |
29
|
adantr |
|
31 |
|
eqid |
|
32 |
31 31
|
lmhmf |
|
33 |
12 32
|
syl |
|
34 |
|
fvex |
|
35 |
34 34
|
elmap |
|
36 |
33 35
|
sylibr |
|
37 |
31 31
|
lmhmf |
|
38 |
13 37
|
syl |
|
39 |
34 34
|
elmap |
|
40 |
38 39
|
sylibr |
|
41 |
31 31
|
lmhmf |
|
42 |
15 41
|
syl |
|
43 |
34 34
|
elmap |
|
44 |
42 43
|
sylibr |
|
45 |
31 6
|
mndvass |
|
46 |
30 36 40 44 45
|
syl13anc |
|
47 |
23 26 46
|
3eqtr4d |
|
48 |
17 19 47
|
3eqtr4d |
|
49 |
|
id |
|
50 |
|
eqidd |
|
51 |
|
eqid |
|
52 |
|
eqid |
|
53 |
51 31 52 52
|
0lmhm |
|
54 |
49 49 50 53
|
syl3anc |
|
55 |
1 2 6 7
|
mendplusg |
|
56 |
54 55
|
sylan |
|
57 |
32 35
|
sylibr |
|
58 |
31 6 51
|
mndvlid |
|
59 |
29 57 58
|
syl2an |
|
60 |
56 59
|
eqtrd |
|
61 |
|
eqid |
|
62 |
61
|
invlmhm |
|
63 |
|
lmhmco |
|
64 |
62 63
|
sylan |
|
65 |
1 2 6 7
|
mendplusg |
|
66 |
64 65
|
sylancom |
|
67 |
31 6 61 51
|
grpvlinv |
|
68 |
27 57 67
|
syl2an |
|
69 |
66 68
|
eqtrd |
|
70 |
3 4 11 48 54 60 64 69
|
isgrpd |
|
71 |
|
eqid |
|
72 |
1 2 71
|
mendmulr |
|
73 |
|
lmhmco |
|
74 |
72 73
|
eqeltrd |
|
75 |
74
|
3adant1 |
|
76 |
|
coass |
|
77 |
12 13 72
|
syl2anc |
|
78 |
77
|
oveq1d |
|
79 |
12 13 73
|
syl2anc |
|
80 |
1 2 71
|
mendmulr |
|
81 |
79 15 80
|
syl2anc |
|
82 |
78 81
|
eqtrd |
|
83 |
1 2 71
|
mendmulr |
|
84 |
13 15 83
|
syl2anc |
|
85 |
84
|
oveq2d |
|
86 |
|
lmhmco |
|
87 |
13 15 86
|
syl2anc |
|
88 |
1 2 71
|
mendmulr |
|
89 |
12 87 88
|
syl2anc |
|
90 |
85 89
|
eqtrd |
|
91 |
76 82 90
|
3eqtr4a |
|
92 |
1 2 71
|
mendmulr |
|
93 |
12 21 92
|
syl2anc |
|
94 |
25
|
oveq2d |
|
95 |
|
lmhmco |
|
96 |
12 15 95
|
syl2anc |
|
97 |
1 2 6 7
|
mendplusg |
|
98 |
79 96 97
|
syl2anc |
|
99 |
1 2 71
|
mendmulr |
|
100 |
12 15 99
|
syl2anc |
|
101 |
77 100
|
oveq12d |
|
102 |
|
lmghm |
|
103 |
|
ghmmhm |
|
104 |
12 102 103
|
3syl |
|
105 |
31 6 6
|
mhmvlin |
|
106 |
104 40 44 105
|
syl3anc |
|
107 |
98 101 106
|
3eqtr4d |
|
108 |
93 94 107
|
3eqtr4d |
|
109 |
1 2 71
|
mendmulr |
|
110 |
14 15 109
|
syl2anc |
|
111 |
18
|
oveq1d |
|
112 |
1 2 6 7
|
mendplusg |
|
113 |
96 87 112
|
syl2anc |
|
114 |
100 84
|
oveq12d |
|
115 |
|
ffn |
|
116 |
12 32 115
|
3syl |
|
117 |
|
ffn |
|
118 |
13 37 117
|
3syl |
|
119 |
34
|
a1i |
|
120 |
|
inidm |
|
121 |
116 118 42 119 119 119 120
|
ofco |
|
122 |
113 114 121
|
3eqtr4d |
|
123 |
110 111 122
|
3eqtr4d |
|
124 |
31
|
idlmhm |
|
125 |
1 2 71
|
mendmulr |
|
126 |
124 125
|
sylan |
|
127 |
32
|
adantl |
|
128 |
|
fcoi2 |
|
129 |
127 128
|
syl |
|
130 |
126 129
|
eqtrd |
|
131 |
|
id |
|
132 |
1 2 71
|
mendmulr |
|
133 |
131 124 132
|
syl2anr |
|
134 |
|
fcoi1 |
|
135 |
127 134
|
syl |
|
136 |
133 135
|
eqtrd |
|
137 |
3 4 5 70 75 91 108 123 124 130 136
|
isringd |
|