Step |
Hyp |
Ref |
Expression |
1 |
|
unxpdomlem1.1 |
|
2 |
|
unxpdomlem1.2 |
|
3 |
|
unxpdomlem2.1 |
|
4 |
|
unxpdomlem2.2 |
|
5 |
|
unxpdomlem2.3 |
|
6 |
5
|
adantr |
|
7 |
|
elun1 |
|
8 |
7
|
ad2antrl |
|
9 |
1 2
|
unxpdomlem1 |
|
10 |
8 9
|
syl |
|
11 |
|
iftrue |
|
12 |
11
|
ad2antrl |
|
13 |
10 12
|
eqtrd |
|
14 |
3
|
adantr |
|
15 |
1 2
|
unxpdomlem1 |
|
16 |
14 15
|
syl |
|
17 |
|
iffalse |
|
18 |
17
|
ad2antll |
|
19 |
16 18
|
eqtrd |
|
20 |
13 19
|
eqeq12d |
|
21 |
20
|
biimpa |
|
22 |
|
vex |
|
23 |
|
vex |
|
24 |
|
vex |
|
25 |
23 24
|
ifex |
|
26 |
22 25
|
opth |
|
27 |
21 26
|
sylib |
|
28 |
27
|
simprd |
|
29 |
|
iftrue |
|
30 |
28
|
eqeq1d |
|
31 |
29 30
|
syl5ib |
|
32 |
|
iftrue |
|
33 |
27
|
simpld |
|
34 |
33
|
eqeq1d |
|
35 |
32 34
|
syl5ibr |
|
36 |
31 35
|
syld |
|
37 |
4
|
ad2antrr |
|
38 |
|
equequ1 |
|
39 |
38
|
notbid |
|
40 |
37 39
|
syl5ibrcom |
|
41 |
36 40
|
pm2.65d |
|
42 |
41
|
iffalsed |
|
43 |
|
iffalse |
|
44 |
33
|
eqeq1d |
|
45 |
43 44
|
syl5ibr |
|
46 |
41 45
|
mt3d |
|
47 |
28 42 46
|
3eqtr3d |
|
48 |
6 47
|
mtand |
|