Step |
Hyp |
Ref |
Expression |
1 |
|
unxpdomlem1.1 |
|
2 |
|
unxpdomlem1.2 |
|
3 |
|
1sdom |
|
4 |
3
|
elv |
|
5 |
|
1sdom |
|
6 |
5
|
elv |
|
7 |
|
reeanv |
|
8 |
|
reeanv |
|
9 |
|
vex |
|
10 |
|
vex |
|
11 |
9 10
|
unex |
|
12 |
9 10
|
xpex |
|
13 |
|
simpr |
|
14 |
|
simp2r |
|
15 |
|
simp1r |
|
16 |
14 15
|
ifcld |
|
17 |
16
|
ad2antrr |
|
18 |
13 17
|
opelxpd |
|
19 |
|
simp2l |
|
20 |
|
simp1l |
|
21 |
19 20
|
ifcld |
|
22 |
21
|
ad2antrr |
|
23 |
|
simpr |
|
24 |
|
elun |
|
25 |
23 24
|
sylib |
|
26 |
25
|
orcanai |
|
27 |
22 26
|
opelxpd |
|
28 |
18 27
|
ifclda |
|
29 |
2 28
|
eqeltrid |
|
30 |
29 1
|
fmptd |
|
31 |
1 2
|
unxpdomlem1 |
|
32 |
31
|
ad2antrl |
|
33 |
|
iftrue |
|
34 |
33
|
adantr |
|
35 |
32 34
|
sylan9eq |
|
36 |
1 2
|
unxpdomlem1 |
|
37 |
36
|
ad2antll |
|
38 |
|
iftrue |
|
39 |
38
|
adantl |
|
40 |
37 39
|
sylan9eq |
|
41 |
35 40
|
eqeq12d |
|
42 |
|
vex |
|
43 |
|
vex |
|
44 |
|
vex |
|
45 |
43 44
|
ifex |
|
46 |
42 45
|
opth1 |
|
47 |
41 46
|
syl6bi |
|
48 |
|
simprr |
|
49 |
|
simpll |
|
50 |
|
simplr |
|
51 |
1 2 48 49 50
|
unxpdomlem2 |
|
52 |
51
|
pm2.21d |
|
53 |
|
eqcom |
|
54 |
|
simprl |
|
55 |
1 2 54 49 50
|
unxpdomlem2 |
|
56 |
55
|
ancom2s |
|
57 |
56
|
pm2.21d |
|
58 |
53 57
|
syl5bi |
|
59 |
|
iffalse |
|
60 |
59
|
adantr |
|
61 |
32 60
|
sylan9eq |
|
62 |
|
iffalse |
|
63 |
62
|
adantl |
|
64 |
37 63
|
sylan9eq |
|
65 |
61 64
|
eqeq12d |
|
66 |
|
vex |
|
67 |
|
vex |
|
68 |
66 67
|
ifex |
|
69 |
68 42
|
opth |
|
70 |
69
|
simprbi |
|
71 |
65 70
|
syl6bi |
|
72 |
47 52 58 71
|
4casesdan |
|
73 |
72
|
ralrimivva |
|
74 |
73
|
3ad2ant3 |
|
75 |
|
dff13 |
|
76 |
30 74 75
|
sylanbrc |
|
77 |
|
f1dom2g |
|
78 |
11 12 76 77
|
mp3an12i |
|
79 |
78
|
3expia |
|
80 |
79
|
rexlimdvva |
|
81 |
8 80
|
syl5bir |
|
82 |
81
|
rexlimivv |
|
83 |
7 82
|
sylbir |
|
84 |
4 6 83
|
syl2anb |
|