Step |
Hyp |
Ref |
Expression |
1 |
|
setsms.x |
|
2 |
|
setsms.d |
|
3 |
|
setsms.k |
|
4 |
|
setsms.m |
|
5 |
1 2 3 4
|
setsmstset |
|
6 |
|
df-mopn |
|
7 |
6
|
dmmptss |
|
8 |
7
|
sseli |
|
9 |
|
simpr |
|
10 |
|
xmetunirn |
|
11 |
9 10
|
sylib |
|
12 |
|
eqid |
|
13 |
12
|
mopnuni |
|
14 |
11 13
|
syl |
|
15 |
2
|
dmeqd |
|
16 |
|
dmres |
|
17 |
15 16
|
eqtrdi |
|
18 |
|
inss1 |
|
19 |
17 18
|
eqsstrdi |
|
20 |
|
dmss |
|
21 |
19 20
|
syl |
|
22 |
|
dmxpid |
|
23 |
21 22
|
sseqtrdi |
|
24 |
23
|
adantr |
|
25 |
14 24
|
eqsstrrd |
|
26 |
|
sspwuni |
|
27 |
25 26
|
sylibr |
|
28 |
27
|
ex |
|
29 |
8 28
|
syl5 |
|
30 |
|
ndmfv |
|
31 |
|
0ss |
|
32 |
30 31
|
eqsstrdi |
|
33 |
29 32
|
pm2.61d1 |
|
34 |
1 2 3
|
setsmsbas |
|
35 |
34
|
pweqd |
|
36 |
33 5 35
|
3sstr3d |
|
37 |
|
eqid |
|
38 |
|
eqid |
|
39 |
37 38
|
topnid |
|
40 |
36 39
|
syl |
|
41 |
5 40
|
eqtrd |
|