Step |
Hyp |
Ref |
Expression |
1 |
|
erclwwlkn.w |
|
2 |
|
erclwwlkn.r |
|
3 |
1 2
|
eclclwwlkn1 |
|
4 |
|
eqeq1 |
|
5 |
4
|
rexbidv |
|
6 |
5
|
elrab |
|
7 |
|
oveq2 |
|
8 |
7
|
eqeq2d |
|
9 |
8
|
cbvrexvw |
|
10 |
|
eqeq1 |
|
11 |
10
|
rexbidv |
|
12 |
11
|
elrab |
|
13 |
|
oveq2 |
|
14 |
13
|
eqeq2d |
|
15 |
14
|
cbvrexvw |
|
16 |
1
|
eleclclwwlknlem2 |
|
17 |
16
|
ex |
|
18 |
17
|
rexlimiva |
|
19 |
15 18
|
sylbi |
|
20 |
19
|
expd |
|
21 |
20
|
impcom |
|
22 |
12 21
|
sylbi |
|
23 |
22
|
com12 |
|
24 |
23
|
ad2antlr |
|
25 |
24
|
imp |
|
26 |
9 25
|
syl5bb |
|
27 |
26
|
anbi2d |
|
28 |
6 27
|
syl5bb |
|
29 |
28
|
ex |
|
30 |
|
eleq2 |
|
31 |
|
eleq2 |
|
32 |
31
|
bibi1d |
|
33 |
30 32
|
imbi12d |
|
34 |
33
|
adantl |
|
35 |
29 34
|
mpbird |
|
36 |
35
|
rexlimdva2 |
|
37 |
3 36
|
sylbid |
|
38 |
37
|
pm2.43i |
|
39 |
38
|
imp |
|