Step |
Hyp |
Ref |
Expression |
1 |
|
df-on |
|
2 |
|
tz7.7 |
|
3 |
|
df-pss |
|
4 |
2 3
|
bitr4di |
|
5 |
4
|
exbiri |
|
6 |
5
|
com23 |
|
7 |
6
|
impd |
|
8 |
7
|
alrimiv |
|
9 |
|
vex |
|
10 |
|
dfon2lem3 |
|
11 |
9 10
|
ax-mp |
|
12 |
11
|
simpld |
|
13 |
9
|
dfon2lem7 |
|
14 |
13
|
ralrimiv |
|
15 |
|
dfon2lem9 |
|
16 |
|
psseq2 |
|
17 |
16
|
anbi1d |
|
18 |
|
elequ2 |
|
19 |
17 18
|
imbi12d |
|
20 |
19
|
albidv |
|
21 |
|
psseq1 |
|
22 |
|
treq |
|
23 |
21 22
|
anbi12d |
|
24 |
|
elequ1 |
|
25 |
23 24
|
imbi12d |
|
26 |
25
|
cbvalvw |
|
27 |
20 26
|
syl6bb |
|
28 |
27
|
rspccv |
|
29 |
|
psseq2 |
|
30 |
29
|
anbi1d |
|
31 |
|
elequ2 |
|
32 |
30 31
|
imbi12d |
|
33 |
32
|
albidv |
|
34 |
|
psseq1 |
|
35 |
|
treq |
|
36 |
34 35
|
anbi12d |
|
37 |
|
elequ1 |
|
38 |
36 37
|
imbi12d |
|
39 |
38
|
cbvalvw |
|
40 |
33 39
|
syl6bb |
|
41 |
40
|
rspccv |
|
42 |
28 41
|
anim12d |
|
43 |
|
vex |
|
44 |
|
vex |
|
45 |
43 44
|
dfon2lem5 |
|
46 |
42 45
|
syl6 |
|
47 |
46
|
ralrimivv |
|
48 |
15 47
|
jca |
|
49 |
14 48
|
syl |
|
50 |
|
dfwe2 |
|
51 |
|
epel |
|
52 |
|
biid |
|
53 |
|
epel |
|
54 |
51 52 53
|
3orbi123i |
|
55 |
54
|
2ralbii |
|
56 |
55
|
anbi2i |
|
57 |
50 56
|
bitri |
|
58 |
49 57
|
sylibr |
|
59 |
|
df-ord |
|
60 |
12 58 59
|
sylanbrc |
|
61 |
8 60
|
impbii |
|
62 |
61
|
abbii |
|
63 |
1 62
|
eqtri |
|