Step |
Hyp |
Ref |
Expression |
1 |
|
umgr2v2evtx.g |
|
2 |
1
|
umgr2v2e |
|
3 |
1
|
umgr2v2evtxel |
|
4 |
3
|
3adant3 |
|
5 |
4
|
adantr |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
6 7 8 9
|
vtxdumgrval |
|
11 |
2 5 10
|
syl2anc |
|
12 |
1
|
umgr2v2eiedg |
|
13 |
12
|
dmeqd |
|
14 |
|
prex |
|
15 |
14 14
|
dmprop |
|
16 |
13 15
|
eqtrdi |
|
17 |
12
|
fveq1d |
|
18 |
17
|
eleq2d |
|
19 |
16 18
|
rabeqbidv |
|
20 |
19
|
fveq2d |
|
21 |
|
prid1g |
|
22 |
|
0ne1 |
|
23 |
|
c0ex |
|
24 |
23 14
|
fvpr1 |
|
25 |
22 24
|
ax-mp |
|
26 |
21 25
|
eleqtrrdi |
|
27 |
|
1ex |
|
28 |
27 14
|
fvpr2 |
|
29 |
22 28
|
ax-mp |
|
30 |
21 29
|
eleqtrrdi |
|
31 |
|
fveq2 |
|
32 |
31
|
eleq2d |
|
33 |
|
fveq2 |
|
34 |
33
|
eleq2d |
|
35 |
23 27 32 34
|
ralpr |
|
36 |
26 30 35
|
sylanbrc |
|
37 |
|
rabid2 |
|
38 |
36 37
|
sylibr |
|
39 |
38
|
eqcomd |
|
40 |
39
|
fveq2d |
|
41 |
|
prhash2ex |
|
42 |
40 41
|
eqtrdi |
|
43 |
42
|
3ad2ant2 |
|
44 |
20 43
|
eqtrd |
|
45 |
44
|
adantr |
|
46 |
11 45
|
eqtrd |
|