Step |
Hyp |
Ref |
Expression |
1 |
|
isomushgr.v |
|
2 |
|
isomushgr.w |
|
3 |
|
isomushgr.e |
|
4 |
|
isomushgr.k |
|
5 |
|
isomuspgrlem2.g |
|
6 |
|
isomuspgrlem2.a |
|
7 |
|
isomuspgrlem2.f |
|
8 |
|
isomuspgrlem2.i |
|
9 |
|
isomuspgrlem2.x |
|
10 |
|
isomuspgrlem2.b |
|
11 |
1 2 3 4 5 6 7 8
|
isomuspgrlem2b |
|
12 |
|
uspgrupgr |
|
13 |
10 12
|
syl |
|
14 |
2 4
|
upgredg |
|
15 |
13 14
|
sylan |
|
16 |
|
eleq1 |
|
17 |
16
|
anbi2d |
|
18 |
|
f1ofo |
|
19 |
7 18
|
syl |
|
20 |
|
foelrn |
|
21 |
19 20
|
sylan |
|
22 |
21
|
ex |
|
23 |
|
foelrn |
|
24 |
19 23
|
sylan |
|
25 |
24
|
ex |
|
26 |
22 25
|
anim12d |
|
27 |
26
|
adantr |
|
28 |
27
|
imp |
|
29 |
|
preq12 |
|
30 |
29
|
ancoms |
|
31 |
30
|
eleq1d |
|
32 |
|
preq1 |
|
33 |
32
|
eleq1d |
|
34 |
|
fveq2 |
|
35 |
34
|
preq1d |
|
36 |
35
|
eleq1d |
|
37 |
33 36
|
bibi12d |
|
38 |
|
preq2 |
|
39 |
38
|
eleq1d |
|
40 |
|
fveq2 |
|
41 |
40
|
preq2d |
|
42 |
41
|
eleq1d |
|
43 |
39 42
|
bibi12d |
|
44 |
37 43
|
rspc2va |
|
45 |
44
|
bicomd |
|
46 |
45
|
ancoms |
|
47 |
46
|
biimpd |
|
48 |
47
|
ex |
|
49 |
8 48
|
syl |
|
50 |
49
|
com13 |
|
51 |
31 50
|
syl6bi |
|
52 |
51
|
com14 |
|
53 |
52
|
imp |
|
54 |
53
|
adantr |
|
55 |
54
|
imp31 |
|
56 |
|
imaeq2 |
|
57 |
|
f1ofn |
|
58 |
7 57
|
syl |
|
59 |
58
|
ad3antrrr |
|
60 |
|
simprl |
|
61 |
|
simpr |
|
62 |
61
|
adantl |
|
63 |
59 60 62
|
3jca |
|
64 |
63
|
adantr |
|
65 |
|
fnimapr |
|
66 |
64 65
|
syl |
|
67 |
56 66
|
sylan9eqr |
|
68 |
67
|
eqeq2d |
|
69 |
30
|
adantl |
|
70 |
55 68 69
|
rspcedvd |
|
71 |
70
|
ex |
|
72 |
71
|
anassrs |
|
73 |
72
|
expd |
|
74 |
73
|
rexlimdva |
|
75 |
74
|
com23 |
|
76 |
75
|
rexlimdva |
|
77 |
76
|
impd |
|
78 |
28 77
|
mpd |
|
79 |
78
|
ex |
|
80 |
17 79
|
syl6bi |
|
81 |
80
|
impd |
|
82 |
81
|
impcom |
|
83 |
|
simpr |
|
84 |
83
|
adantr |
|
85 |
9
|
ad4antr |
|
86 |
1 2 3 4 5
|
isomuspgrlem2a |
|
87 |
85 86
|
syl |
|
88 |
|
imaeq2 |
|
89 |
|
fveq2 |
|
90 |
88 89
|
eqeq12d |
|
91 |
90
|
rspcv |
|
92 |
|
eqcom |
|
93 |
91 92
|
syl6ibr |
|
94 |
93
|
adantl |
|
95 |
87 94
|
mpd |
|
96 |
84 95
|
eqeq12d |
|
97 |
96
|
rexbidva |
|
98 |
82 97
|
mpbird |
|
99 |
98
|
ex |
|
100 |
99
|
rexlimdvva |
|
101 |
15 100
|
mpd |
|
102 |
101
|
ralrimiva |
|
103 |
|
dffo3 |
|
104 |
11 102 103
|
sylanbrc |
|