Step |
Hyp |
Ref |
Expression |
1 |
|
isubgredg.v |
|
2 |
|
isubgredg.e |
|
3 |
|
isubgredg.h |
|
4 |
|
isubgredg.i |
|
5 |
3
|
fveq2i |
|
6 |
|
eqid |
|
7 |
1 6
|
isubgriedg |
|
8 |
5 7
|
eqtrid |
|
9 |
8
|
rneqd |
|
10 |
9
|
eleq2d |
|
11 |
1 6
|
uhgrf |
|
12 |
11
|
adantr |
|
13 |
12
|
ffnd |
|
14 |
|
ssrab2 |
|
15 |
14
|
a1i |
|
16 |
13 15
|
fnssresd |
|
17 |
|
fvelrnb |
|
18 |
16 17
|
syl |
|
19 |
|
fvres |
|
20 |
19
|
adantl |
|
21 |
20
|
eqeq1d |
|
22 |
|
fveq2 |
|
23 |
22
|
sseq1d |
|
24 |
23
|
elrab |
|
25 |
6
|
uhgrfun |
|
26 |
25
|
adantr |
|
27 |
|
simpl |
|
28 |
|
fvelrn |
|
29 |
26 27 28
|
syl2anr |
|
30 |
|
simpr |
|
31 |
30
|
adantr |
|
32 |
29 31
|
jca |
|
33 |
32
|
ex |
|
34 |
24 33
|
sylbi |
|
35 |
34
|
impcom |
|
36 |
|
eleq1 |
|
37 |
|
sseq1 |
|
38 |
36 37
|
anbi12d |
|
39 |
35 38
|
syl5ibcom |
|
40 |
21 39
|
sylbid |
|
41 |
40
|
rexlimdva |
|
42 |
|
edgval |
|
43 |
42
|
eqcomi |
|
44 |
43
|
eleq2i |
|
45 |
6
|
edgiedgb |
|
46 |
44 45
|
bitrid |
|
47 |
25 46
|
syl |
|
48 |
47
|
adantr |
|
49 |
|
simprl |
|
50 |
|
simpr |
|
51 |
50
|
sseq1d |
|
52 |
51
|
biimpcd |
|
53 |
52
|
adantl |
|
54 |
53
|
imp |
|
55 |
49 54 24
|
sylanbrc |
|
56 |
|
simpr |
|
57 |
50
|
eqcomd |
|
58 |
57
|
adantl |
|
59 |
19 58
|
sylan9eqr |
|
60 |
56 59
|
jca |
|
61 |
55 60
|
mpdan |
|
62 |
61
|
ex |
|
63 |
62
|
eximdv |
|
64 |
|
df-rex |
|
65 |
|
df-rex |
|
66 |
63 64 65
|
3imtr4g |
|
67 |
66
|
ex |
|
68 |
67
|
com23 |
|
69 |
48 68
|
sylbid |
|
70 |
69
|
impd |
|
71 |
41 70
|
impbid |
|
72 |
10 18 71
|
3bitrd |
|
73 |
|
edgval |
|
74 |
4 73
|
eqtri |
|
75 |
74
|
eleq2i |
|
76 |
2 42
|
eqtri |
|
77 |
76
|
eleq2i |
|
78 |
77
|
anbi1i |
|
79 |
72 75 78
|
3bitr4g |
|