Step |
Hyp |
Ref |
Expression |
1 |
|
0elpw |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
2 3 4
|
lcoop |
|
6 |
1 5
|
mpan2 |
|
7 |
|
fvex |
|
8 |
|
map0e |
|
9 |
7 8
|
mp1i |
|
10 |
|
df1o2 |
|
11 |
9 10
|
eqtrdi |
|
12 |
11
|
rexeqdv |
|
13 |
|
lincval0 |
|
14 |
13
|
adantr |
|
15 |
14
|
eqeq2d |
|
16 |
15
|
anbi2d |
|
17 |
|
0ex |
|
18 |
|
breq1 |
|
19 |
|
fvex |
|
20 |
|
0fsupp |
|
21 |
19 20
|
ax-mp |
|
22 |
|
0fin |
|
23 |
21 22
|
2th |
|
24 |
18 23
|
syl6bb |
|
25 |
|
oveq1 |
|
26 |
25
|
eqeq2d |
|
27 |
24 26
|
anbi12d |
|
28 |
27
|
rexsng |
|
29 |
17 28
|
mp1i |
|
30 |
22
|
a1i |
|
31 |
30
|
biantrurd |
|
32 |
16 29 31
|
3bitr4d |
|
33 |
12 32
|
bitrd |
|
34 |
33
|
rabbidva |
|
35 |
|
eqid |
|
36 |
2 35
|
mndidcl |
|
37 |
|
rabsn |
|
38 |
36 37
|
syl |
|
39 |
6 34 38
|
3eqtrd |
|