Step |
Hyp |
Ref |
Expression |
1 |
|
amgmlemALT.0 |
|
2 |
|
amgmlemALT.1 |
|
3 |
|
amgmlemALT.2 |
|
4 |
|
amgmlemALT.3 |
|
5 |
|
hashnncl |
|
6 |
2 5
|
syl |
|
7 |
3 6
|
mpbird |
|
8 |
7
|
nnrpd |
|
9 |
8
|
rpreccld |
|
10 |
|
fconst6g |
|
11 |
9 10
|
syl |
|
12 |
|
fconstmpt |
|
13 |
12
|
a1i |
|
14 |
13
|
oveq2d |
|
15 |
7
|
nnrecred |
|
16 |
15
|
recnd |
|
17 |
|
simpl |
|
18 |
|
simplr |
|
19 |
17 18
|
gsumfsum |
|
20 |
2 16 19
|
syl2anc |
|
21 |
|
fsumconst |
|
22 |
2 16 21
|
syl2anc |
|
23 |
7
|
nncnd |
|
24 |
7
|
nnne0d |
|
25 |
23 24
|
recidd |
|
26 |
22 25
|
eqtrd |
|
27 |
14 20 26
|
3eqtrd |
|
28 |
1 2 3 4 11 27
|
amgmwlem |
|
29 |
|
rpssre |
|
30 |
|
ax-resscn |
|
31 |
29 30
|
sstri |
|
32 |
|
eqid |
|
33 |
|
cnfldbas |
|
34 |
1 33
|
mgpbas |
|
35 |
32 34
|
ressbas2 |
|
36 |
31 35
|
ax-mp |
|
37 |
|
cnfld1 |
|
38 |
1 37
|
ringidval |
|
39 |
1
|
oveq1i |
|
40 |
39
|
rpmsubg |
|
41 |
|
subgsubm |
|
42 |
40 41
|
ax-mp |
|
43 |
|
cnring |
|
44 |
|
cnfld0 |
|
45 |
|
cndrng |
|
46 |
33 44 45
|
drngui |
|
47 |
46 1
|
unitsubm |
|
48 |
43 47
|
ax-mp |
|
49 |
|
eqid |
|
50 |
49
|
subsubm |
|
51 |
48 50
|
ax-mp |
|
52 |
42 51
|
mpbi |
|
53 |
52
|
simpli |
|
54 |
|
eqid |
|
55 |
32 54
|
subm0 |
|
56 |
53 55
|
ax-mp |
|
57 |
38 56
|
eqtri |
|
58 |
|
cncrng |
|
59 |
1
|
crngmgp |
|
60 |
58 59
|
ax-mp |
|
61 |
32
|
submmnd |
|
62 |
53 61
|
mp1i |
|
63 |
32
|
subcmn |
|
64 |
60 62 63
|
sylancr |
|
65 |
|
reex |
|
66 |
65 29
|
ssexi |
|
67 |
|
cnfldmul |
|
68 |
1 67
|
mgpplusg |
|
69 |
32 68
|
ressplusg |
|
70 |
66 69
|
ax-mp |
|
71 |
|
eqid |
|
72 |
71
|
rpmsubg |
|
73 |
1
|
oveq1i |
|
74 |
|
cnex |
|
75 |
|
difss |
|
76 |
74 75
|
ssexi |
|
77 |
|
rpcndif0 |
|
78 |
77
|
ssriv |
|
79 |
|
ressabs |
|
80 |
76 78 79
|
mp2an |
|
81 |
73 80
|
eqtr4i |
|
82 |
81
|
subggrp |
|
83 |
72 82
|
mp1i |
|
84 |
|
simpr |
|
85 |
15
|
adantr |
|
86 |
84 85
|
rpcxpcld |
|
87 |
|
eqid |
|
88 |
86 87
|
fmptd |
|
89 |
|
simprl |
|
90 |
89
|
rprege0d |
|
91 |
|
simprr |
|
92 |
91
|
rprege0d |
|
93 |
16
|
adantr |
|
94 |
|
mulcxp |
|
95 |
90 92 93 94
|
syl3anc |
|
96 |
|
rpmulcl |
|
97 |
96
|
adantl |
|
98 |
|
oveq1 |
|
99 |
|
ovex |
|
100 |
98 87 99
|
fvmpt3i |
|
101 |
97 100
|
syl |
|
102 |
|
oveq1 |
|
103 |
102 87 99
|
fvmpt3i |
|
104 |
89 103
|
syl |
|
105 |
|
oveq1 |
|
106 |
105 87 99
|
fvmpt3i |
|
107 |
91 106
|
syl |
|
108 |
104 107
|
oveq12d |
|
109 |
95 101 108
|
3eqtr4d |
|
110 |
36 36 70 70 83 83 88 109
|
isghmd |
|
111 |
|
ghmmhm |
|
112 |
110 111
|
syl |
|
113 |
|
1red |
|
114 |
4 2 113
|
fdmfifsupp |
|
115 |
36 57 64 62 2 112 4 114
|
gsummhm |
|
116 |
53
|
a1i |
|
117 |
4
|
ffvelrnda |
|
118 |
15
|
adantr |
|
119 |
117 118
|
rpcxpcld |
|
120 |
|
eqid |
|
121 |
119 120
|
fmptd |
|
122 |
2 116 121 32
|
gsumsubm |
|
123 |
9
|
adantr |
|
124 |
4
|
feqmptd |
|
125 |
2 117 123 124 13
|
offval2 |
|
126 |
125
|
oveq2d |
|
127 |
102
|
cbvmptv |
|
128 |
127
|
a1i |
|
129 |
|
oveq1 |
|
130 |
117 124 128 129
|
fmptco |
|
131 |
130
|
oveq2d |
|
132 |
122 126 131
|
3eqtr4rd |
|
133 |
36 57 64 2 4 114
|
gsumcl |
|
134 |
|
oveq1 |
|
135 |
134 87 99
|
fvmpt3i |
|
136 |
133 135
|
syl |
|
137 |
2 116 4 32
|
gsumsubm |
|
138 |
137
|
oveq1d |
|
139 |
136 138
|
eqtr4d |
|
140 |
115 132 139
|
3eqtr3d |
|
141 |
117
|
rpcnd |
|
142 |
2 141
|
fsumcl |
|
143 |
142 23 24
|
divrecd |
|
144 |
2 16 141
|
fsummulc1 |
|
145 |
143 144
|
eqtr2d |
|
146 |
16
|
adantr |
|
147 |
141 146
|
mulcld |
|
148 |
2 147
|
gsumfsum |
|
149 |
2 141
|
gsumfsum |
|
150 |
149
|
oveq1d |
|
151 |
145 148 150
|
3eqtr4d |
|
152 |
2 117 146 124 13
|
offval2 |
|
153 |
152
|
oveq2d |
|
154 |
124
|
oveq2d |
|
155 |
154
|
oveq1d |
|
156 |
151 153 155
|
3eqtr4d |
|
157 |
28 140 156
|
3brtr3d |
|