Step |
Hyp |
Ref |
Expression |
1 |
|
nbgr2vtx1edg.v |
|
2 |
|
nbgr2vtx1edg.e |
|
3 |
1
|
fvexi |
|
4 |
|
hash2prb |
|
5 |
3 4
|
ax-mp |
|
6 |
|
simpr |
|
7 |
6
|
ancomd |
|
8 |
7
|
ad2antrr |
|
9 |
|
id |
|
10 |
9
|
necomd |
|
11 |
10
|
adantr |
|
12 |
11
|
ad2antlr |
|
13 |
|
prcom |
|
14 |
13
|
eleq1i |
|
15 |
14
|
biimpi |
|
16 |
|
sseq2 |
|
17 |
16
|
adantl |
|
18 |
13
|
eqimssi |
|
19 |
18
|
a1i |
|
20 |
15 17 19
|
rspcedvd |
|
21 |
20
|
adantl |
|
22 |
1 2
|
nbgrel |
|
23 |
8 12 21 22
|
syl3anbrc |
|
24 |
6
|
ad2antrr |
|
25 |
|
simplrl |
|
26 |
|
id |
|
27 |
|
sseq2 |
|
28 |
27
|
adantl |
|
29 |
|
prcom |
|
30 |
29
|
eqimssi |
|
31 |
30
|
a1i |
|
32 |
26 28 31
|
rspcedvd |
|
33 |
32
|
adantl |
|
34 |
1 2
|
nbgrel |
|
35 |
24 25 33 34
|
syl3anbrc |
|
36 |
23 35
|
jca |
|
37 |
36
|
ex |
|
38 |
1 2
|
nbuhgr2vtx1edgblem |
|
39 |
38
|
3exp |
|
40 |
39
|
adantr |
|
41 |
40
|
adantld |
|
42 |
41
|
imp |
|
43 |
42
|
adantld |
|
44 |
37 43
|
impbid |
|
45 |
|
eleq1 |
|
46 |
45
|
adantl |
|
47 |
|
id |
|
48 |
|
difeq1 |
|
49 |
48
|
raleqdv |
|
50 |
47 49
|
raleqbidv |
|
51 |
|
vex |
|
52 |
|
vex |
|
53 |
|
sneq |
|
54 |
53
|
difeq2d |
|
55 |
|
oveq2 |
|
56 |
55
|
eleq2d |
|
57 |
54 56
|
raleqbidv |
|
58 |
|
sneq |
|
59 |
58
|
difeq2d |
|
60 |
|
oveq2 |
|
61 |
60
|
eleq2d |
|
62 |
59 61
|
raleqbidv |
|
63 |
51 52 57 62
|
ralpr |
|
64 |
|
difprsn1 |
|
65 |
64
|
raleqdv |
|
66 |
|
eleq1 |
|
67 |
52 66
|
ralsn |
|
68 |
65 67
|
syl6bb |
|
69 |
|
difprsn2 |
|
70 |
69
|
raleqdv |
|
71 |
|
eleq1 |
|
72 |
51 71
|
ralsn |
|
73 |
70 72
|
syl6bb |
|
74 |
68 73
|
anbi12d |
|
75 |
63 74
|
syl5bb |
|
76 |
50 75
|
sylan9bbr |
|
77 |
46 76
|
bibi12d |
|
78 |
77
|
adantl |
|
79 |
44 78
|
mpbird |
|
80 |
79
|
ex |
|
81 |
80
|
rexlimdvva |
|
82 |
5 81
|
syl5bi |
|
83 |
82
|
imp |
|