Step |
Hyp |
Ref |
Expression |
1 |
|
frgpup.b |
|
2 |
|
frgpup.n |
|
3 |
|
frgpup.t |
|
4 |
|
frgpup.h |
|
5 |
|
frgpup.i |
|
6 |
|
frgpup.a |
|
7 |
|
frgpuptinv.m |
|
8 |
|
elxp2 |
|
9 |
7
|
efgmval |
|
10 |
9
|
adantl |
|
11 |
10
|
fveq2d |
|
12 |
|
df-ov |
|
13 |
11 12
|
eqtr4di |
|
14 |
|
elpri |
|
15 |
|
df2o3 |
|
16 |
14 15
|
eleq2s |
|
17 |
|
simpr |
|
18 |
|
1oex |
|
19 |
18
|
prid2 |
|
20 |
19 15
|
eleqtrri |
|
21 |
|
1n0 |
|
22 |
|
neeq1 |
|
23 |
21 22
|
mpbiri |
|
24 |
|
ifnefalse |
|
25 |
23 24
|
syl |
|
26 |
|
fveq2 |
|
27 |
26
|
fveq2d |
|
28 |
25 27
|
sylan9eqr |
|
29 |
|
fvex |
|
30 |
28 3 29
|
ovmpoa |
|
31 |
17 20 30
|
sylancl |
|
32 |
|
0ex |
|
33 |
32
|
prid1 |
|
34 |
33 15
|
eleqtrri |
|
35 |
|
iftrue |
|
36 |
35 26
|
sylan9eqr |
|
37 |
|
fvex |
|
38 |
36 3 37
|
ovmpoa |
|
39 |
17 34 38
|
sylancl |
|
40 |
39
|
fveq2d |
|
41 |
31 40
|
eqtr4d |
|
42 |
|
difeq2 |
|
43 |
|
dif0 |
|
44 |
42 43
|
eqtrdi |
|
45 |
44
|
oveq2d |
|
46 |
|
oveq2 |
|
47 |
46
|
fveq2d |
|
48 |
45 47
|
eqeq12d |
|
49 |
41 48
|
syl5ibrcom |
|
50 |
41
|
fveq2d |
|
51 |
6
|
ffvelrnda |
|
52 |
39 51
|
eqeltrd |
|
53 |
1 2
|
grpinvinv |
|
54 |
4 52 53
|
syl2an2r |
|
55 |
50 54
|
eqtr2d |
|
56 |
|
difeq2 |
|
57 |
|
difid |
|
58 |
56 57
|
eqtrdi |
|
59 |
58
|
oveq2d |
|
60 |
|
oveq2 |
|
61 |
60
|
fveq2d |
|
62 |
59 61
|
eqeq12d |
|
63 |
55 62
|
syl5ibrcom |
|
64 |
49 63
|
jaod |
|
65 |
16 64
|
syl5 |
|
66 |
65
|
impr |
|
67 |
13 66
|
eqtrd |
|
68 |
|
fveq2 |
|
69 |
|
df-ov |
|
70 |
68 69
|
eqtr4di |
|
71 |
70
|
fveq2d |
|
72 |
|
fveq2 |
|
73 |
|
df-ov |
|
74 |
72 73
|
eqtr4di |
|
75 |
74
|
fveq2d |
|
76 |
71 75
|
eqeq12d |
|
77 |
67 76
|
syl5ibrcom |
|
78 |
77
|
rexlimdvva |
|
79 |
8 78
|
syl5bi |
|
80 |
79
|
imp |
|