Step |
Hyp |
Ref |
Expression |
1 |
|
sdomdom |
|
2 |
|
relsdom |
|
3 |
2
|
brrelex2i |
|
4 |
|
brdomg |
|
5 |
3 4
|
syl |
|
6 |
1 5
|
mpbid |
|
7 |
6
|
adantr |
|
8 |
|
f1f |
|
9 |
8
|
frnd |
|
10 |
9
|
adantl |
|
11 |
|
sdomnen |
|
12 |
11
|
ad2antrr |
|
13 |
|
vex |
|
14 |
|
dff1o5 |
|
15 |
14
|
biimpri |
|
16 |
|
f1oen3g |
|
17 |
13 15 16
|
sylancr |
|
18 |
17
|
ex |
|
19 |
18
|
necon3bd |
|
20 |
19
|
adantl |
|
21 |
12 20
|
mpd |
|
22 |
|
pssdifn0 |
|
23 |
10 21 22
|
syl2anc |
|
24 |
|
n0 |
|
25 |
23 24
|
sylib |
|
26 |
2
|
brrelex1i |
|
27 |
26
|
ad2antrr |
|
28 |
3
|
ad2antrr |
|
29 |
|
difexg |
|
30 |
28 29
|
syl |
|
31 |
|
eldifn |
|
32 |
|
disjsn |
|
33 |
31 32
|
sylibr |
|
34 |
33
|
adantl |
|
35 |
9
|
adantr |
|
36 |
|
reldisj |
|
37 |
35 36
|
syl |
|
38 |
34 37
|
mpbid |
|
39 |
|
f1ssr |
|
40 |
38 39
|
syldan |
|
41 |
40
|
adantl |
|
42 |
|
f1dom2g |
|
43 |
27 30 41 42
|
syl3anc |
|
44 |
|
eldifi |
|
45 |
44
|
ad2antll |
|
46 |
|
simplr |
|
47 |
|
difsnen |
|
48 |
28 45 46 47
|
syl3anc |
|
49 |
|
domentr |
|
50 |
43 48 49
|
syl2anc |
|
51 |
50
|
expr |
|
52 |
51
|
exlimdv |
|
53 |
25 52
|
mpd |
|
54 |
7 53
|
exlimddv |
|
55 |
1
|
adantr |
|
56 |
|
difsn |
|
57 |
56
|
breq2d |
|
58 |
57
|
adantl |
|
59 |
55 58
|
mpbird |
|
60 |
54 59
|
pm2.61dan |
|