Step |
Hyp |
Ref |
Expression |
1 |
|
keridl.1 |
|
2 |
|
keridl.2 |
|
3 |
|
cnvimass |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
4 5 1 6
|
rngohomf |
|
8 |
3 7
|
fssdm |
|
9 |
|
eqid |
|
10 |
4 5 9
|
rngo0cl |
|
11 |
10
|
3ad2ant1 |
|
12 |
4 9 1 2
|
rngohom0 |
|
13 |
|
fvex |
|
14 |
13
|
elsn |
|
15 |
12 14
|
sylibr |
|
16 |
|
ffn |
|
17 |
|
elpreima |
|
18 |
7 16 17
|
3syl |
|
19 |
11 15 18
|
mpbir2and |
|
20 |
|
an4 |
|
21 |
4 5 1
|
rngohomadd |
|
22 |
21
|
adantr |
|
23 |
|
oveq12 |
|
24 |
23
|
adantl |
|
25 |
1
|
rngogrpo |
|
26 |
6 2
|
grpoidcl |
|
27 |
6 2
|
grpolid |
|
28 |
25 26 27
|
syl2anc2 |
|
29 |
28
|
3ad2ant2 |
|
30 |
29
|
ad2antrr |
|
31 |
22 24 30
|
3eqtrd |
|
32 |
31
|
ex |
|
33 |
|
fvex |
|
34 |
33
|
elsn |
|
35 |
|
fvex |
|
36 |
35
|
elsn |
|
37 |
34 36
|
anbi12i |
|
38 |
|
fvex |
|
39 |
38
|
elsn |
|
40 |
32 37 39
|
3imtr4g |
|
41 |
40
|
imdistanda |
|
42 |
4 5
|
rngogcl |
|
43 |
42
|
3expib |
|
44 |
43
|
3ad2ant1 |
|
45 |
44
|
anim1d |
|
46 |
41 45
|
syld |
|
47 |
20 46
|
syl5bi |
|
48 |
|
elpreima |
|
49 |
7 16 48
|
3syl |
|
50 |
|
elpreima |
|
51 |
7 16 50
|
3syl |
|
52 |
49 51
|
anbi12d |
|
53 |
|
elpreima |
|
54 |
7 16 53
|
3syl |
|
55 |
47 52 54
|
3imtr4d |
|
56 |
55
|
impl |
|
57 |
56
|
ralrimiva |
|
58 |
34
|
anbi2i |
|
59 |
|
eqid |
|
60 |
4 59 5
|
rngocl |
|
61 |
60
|
3expb |
|
62 |
61
|
3ad2antl1 |
|
63 |
62
|
anass1rs |
|
64 |
63
|
adantlrr |
|
65 |
|
eqid |
|
66 |
4 5 59 65
|
rngohommul |
|
67 |
66
|
anass1rs |
|
68 |
67
|
adantlrr |
|
69 |
|
oveq2 |
|
70 |
69
|
adantl |
|
71 |
70
|
ad2antlr |
|
72 |
4 5 1 6
|
rngohomcl |
|
73 |
2 6 1 65
|
rngorz |
|
74 |
73
|
3ad2antl2 |
|
75 |
72 74
|
syldan |
|
76 |
75
|
adantlr |
|
77 |
68 71 76
|
3eqtrd |
|
78 |
|
fvex |
|
79 |
78
|
elsn |
|
80 |
77 79
|
sylibr |
|
81 |
|
elpreima |
|
82 |
7 16 81
|
3syl |
|
83 |
82
|
ad2antrr |
|
84 |
64 80 83
|
mpbir2and |
|
85 |
4 59 5
|
rngocl |
|
86 |
85
|
3expb |
|
87 |
86
|
3ad2antl1 |
|
88 |
87
|
anassrs |
|
89 |
88
|
adantlrr |
|
90 |
4 5 59 65
|
rngohommul |
|
91 |
90
|
anassrs |
|
92 |
91
|
adantlrr |
|
93 |
|
oveq1 |
|
94 |
93
|
adantl |
|
95 |
94
|
ad2antlr |
|
96 |
2 6 1 65
|
rngolz |
|
97 |
96
|
3ad2antl2 |
|
98 |
72 97
|
syldan |
|
99 |
98
|
adantlr |
|
100 |
92 95 99
|
3eqtrd |
|
101 |
|
fvex |
|
102 |
101
|
elsn |
|
103 |
100 102
|
sylibr |
|
104 |
|
elpreima |
|
105 |
7 16 104
|
3syl |
|
106 |
105
|
ad2antrr |
|
107 |
89 103 106
|
mpbir2and |
|
108 |
84 107
|
jca |
|
109 |
108
|
ralrimiva |
|
110 |
109
|
ex |
|
111 |
58 110
|
syl5bi |
|
112 |
49 111
|
sylbid |
|
113 |
112
|
imp |
|
114 |
57 113
|
jca |
|
115 |
114
|
ralrimiva |
|
116 |
4 59 5 9
|
isidl |
|
117 |
116
|
3ad2ant1 |
|
118 |
8 19 115 117
|
mpbir3and |
|