| 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 |
|