Step |
Hyp |
Ref |
Expression |
1 |
|
1egrvtxdg1.v |
|
2 |
|
1egrvtxdg1.a |
|
3 |
|
1egrvtxdg1.b |
|
4 |
|
1egrvtxdg1.c |
|
5 |
|
1egrvtxdg1.n |
|
6 |
|
1egrvtxdg0.d |
|
7 |
|
1egrvtxdg0.n |
|
8 |
|
1egrvtxdg0.i |
|
9 |
1
|
adantl |
|
10 |
2
|
adantl |
|
11 |
3
|
adantl |
|
12 |
8
|
adantl |
|
13 |
|
preq2 |
|
14 |
13
|
eqcoms |
|
15 |
|
dfsn2 |
|
16 |
14 15
|
eqtr4di |
|
17 |
16
|
adantr |
|
18 |
17
|
opeq2d |
|
19 |
18
|
sneqd |
|
20 |
12 19
|
eqtrd |
|
21 |
5
|
necomd |
|
22 |
4 21
|
jca |
|
23 |
|
eldifsn |
|
24 |
22 23
|
sylibr |
|
25 |
24
|
adantl |
|
26 |
9 10 11 20 25
|
1loopgrvd0 |
|
27 |
26
|
ex |
|
28 |
|
necom |
|
29 |
|
df-ne |
|
30 |
28 29
|
sylbb |
|
31 |
5 30
|
syl |
|
32 |
7
|
neneqd |
|
33 |
31 32
|
jca |
|
34 |
33
|
adantl |
|
35 |
|
ioran |
|
36 |
34 35
|
sylibr |
|
37 |
|
edgval |
|
38 |
8
|
rneqd |
|
39 |
|
rnsnopg |
|
40 |
2 39
|
syl |
|
41 |
38 40
|
eqtrd |
|
42 |
37 41
|
eqtrid |
|
43 |
42
|
adantl |
|
44 |
43
|
rexeqdv |
|
45 |
|
prex |
|
46 |
|
eleq2 |
|
47 |
46
|
rexsng |
|
48 |
45 47
|
mp1i |
|
49 |
|
elprg |
|
50 |
4 49
|
syl |
|
51 |
50
|
adantl |
|
52 |
44 48 51
|
3bitrd |
|
53 |
36 52
|
mtbird |
|
54 |
|
eqid |
|
55 |
2
|
adantl |
|
56 |
3 1
|
eleqtrrd |
|
57 |
56
|
adantl |
|
58 |
6 1
|
eleqtrrd |
|
59 |
58
|
adantl |
|
60 |
8
|
adantl |
|
61 |
|
simpl |
|
62 |
54 55 57 59 60 61
|
usgr1e |
|
63 |
4 1
|
eleqtrrd |
|
64 |
63
|
adantl |
|
65 |
|
eqid |
|
66 |
|
eqid |
|
67 |
54 65 66
|
vtxdusgr0edgnel |
|
68 |
62 64 67
|
syl2anc |
|
69 |
53 68
|
mpbird |
|
70 |
69
|
ex |
|
71 |
27 70
|
pm2.61ine |
|