Step |
Hyp |
Ref |
Expression |
1 |
|
amgm.1 |
|
2 |
|
cnfldbas |
|
3 |
1 2
|
mgpbas |
|
4 |
|
cnfld1 |
|
5 |
1 4
|
ringidval |
|
6 |
|
cnfldmul |
|
7 |
1 6
|
mgpplusg |
|
8 |
|
cncrng |
|
9 |
1
|
crngmgp |
|
10 |
8 9
|
mp1i |
|
11 |
|
simpl1 |
|
12 |
|
simpl3 |
|
13 |
|
rge0ssre |
|
14 |
|
ax-resscn |
|
15 |
13 14
|
sstri |
|
16 |
|
fss |
|
17 |
12 15 16
|
sylancl |
|
18 |
|
1ex |
|
19 |
18
|
a1i |
|
20 |
17 11 19
|
fdmfifsupp |
|
21 |
|
disjdif |
|
22 |
21
|
a1i |
|
23 |
|
undif2 |
|
24 |
|
simprl |
|
25 |
24
|
snssd |
|
26 |
|
ssequn1 |
|
27 |
25 26
|
sylib |
|
28 |
23 27
|
syl5req |
|
29 |
3 5 7 10 11 17 20 22 28
|
gsumsplit |
|
30 |
12 25
|
feqresmpt |
|
31 |
30
|
oveq2d |
|
32 |
|
cnring |
|
33 |
1
|
ringmgp |
|
34 |
32 33
|
mp1i |
|
35 |
17 24
|
ffvelrnd |
|
36 |
|
fveq2 |
|
37 |
3 36
|
gsumsn |
|
38 |
34 24 35 37
|
syl3anc |
|
39 |
|
simprr |
|
40 |
31 38 39
|
3eqtrd |
|
41 |
40
|
oveq1d |
|
42 |
|
diffi |
|
43 |
11 42
|
syl |
|
44 |
|
difss |
|
45 |
|
fssres |
|
46 |
17 44 45
|
sylancl |
|
47 |
46 43 19
|
fdmfifsupp |
|
48 |
3 5 10 43 46 47
|
gsumcl |
|
49 |
48
|
mul02d |
|
50 |
29 41 49
|
3eqtrd |
|
51 |
50
|
oveq1d |
|
52 |
|
simpl2 |
|
53 |
|
hashnncl |
|
54 |
11 53
|
syl |
|
55 |
52 54
|
mpbird |
|
56 |
55
|
nncnd |
|
57 |
55
|
nnne0d |
|
58 |
56 57
|
reccld |
|
59 |
56 57
|
recne0d |
|
60 |
58 59
|
0cxpd |
|
61 |
51 60
|
eqtrd |
|
62 |
|
cnfld0 |
|
63 |
|
ringcmn |
|
64 |
32 63
|
mp1i |
|
65 |
|
rege0subm |
|
66 |
65
|
a1i |
|
67 |
|
c0ex |
|
68 |
67
|
a1i |
|
69 |
12 11 68
|
fdmfifsupp |
|
70 |
62 64 11 66 12 69
|
gsumsubmcl |
|
71 |
|
elrege0 |
|
72 |
70 71
|
sylib |
|
73 |
55
|
nnred |
|
74 |
55
|
nngt0d |
|
75 |
|
divge0 |
|
76 |
72 73 74 75
|
syl12anc |
|
77 |
61 76
|
eqbrtrd |
|
78 |
77
|
rexlimdvaa |
|
79 |
|
ralnex |
|
80 |
|
simpl1 |
|
81 |
|
simpl2 |
|
82 |
|
simpl3 |
|
83 |
82
|
ffnd |
|
84 |
|
ffvelrn |
|
85 |
84
|
3ad2antl3 |
|
86 |
|
elrege0 |
|
87 |
85 86
|
sylib |
|
88 |
87
|
simprd |
|
89 |
|
0re |
|
90 |
87
|
simpld |
|
91 |
|
leloe |
|
92 |
89 90 91
|
sylancr |
|
93 |
88 92
|
mpbid |
|
94 |
93
|
ord |
|
95 |
|
eqcom |
|
96 |
94 95
|
syl6ib |
|
97 |
96
|
con1d |
|
98 |
|
elrp |
|
99 |
98
|
baib |
|
100 |
90 99
|
syl |
|
101 |
97 100
|
sylibrd |
|
102 |
101
|
ralimdva |
|
103 |
102
|
imp |
|
104 |
|
ffnfv |
|
105 |
83 103 104
|
sylanbrc |
|
106 |
1 80 81 105
|
amgmlem |
|
107 |
106
|
ex |
|
108 |
79 107
|
syl5bir |
|
109 |
78 108
|
pm2.61d |
|