Step |
Hyp |
Ref |
Expression |
1 |
|
xkoopn.x |
|
2 |
|
xkoopn.r |
|
3 |
|
xkoopn.s |
|
4 |
|
xkoopn.a |
|
5 |
|
xkoopn.c |
|
6 |
|
xkoopn.u |
|
7 |
|
ovex |
|
8 |
7
|
pwex |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
1 9 10
|
xkotf |
|
12 |
|
frn |
|
13 |
11 12
|
ax-mp |
|
14 |
8 13
|
ssexi |
|
15 |
|
ssfii |
|
16 |
14 15
|
ax-mp |
|
17 |
|
fvex |
|
18 |
|
bastg |
|
19 |
17 18
|
ax-mp |
|
20 |
16 19
|
sstri |
|
21 |
|
oveq2 |
|
22 |
21
|
eleq1d |
|
23 |
1
|
topopn |
|
24 |
|
elpw2g |
|
25 |
2 23 24
|
3syl |
|
26 |
4 25
|
mpbird |
|
27 |
22 26 5
|
elrabd |
|
28 |
|
eqidd |
|
29 |
|
imaeq2 |
|
30 |
29
|
sseq1d |
|
31 |
30
|
rabbidv |
|
32 |
31
|
eqeq2d |
|
33 |
|
sseq2 |
|
34 |
33
|
rabbidv |
|
35 |
34
|
eqeq2d |
|
36 |
32 35
|
rspc2ev |
|
37 |
27 6 28 36
|
syl3anc |
|
38 |
7
|
rabex |
|
39 |
|
eqeq1 |
|
40 |
39
|
2rexbidv |
|
41 |
10
|
rnmpo |
|
42 |
38 40 41
|
elab2 |
|
43 |
37 42
|
sylibr |
|
44 |
20 43
|
sseldi |
|
45 |
1 9 10
|
xkoval |
|
46 |
2 3 45
|
syl2anc |
|
47 |
44 46
|
eleqtrrd |
|