Step |
Hyp |
Ref |
Expression |
1 |
|
satfrel |
|
2 |
1
|
adantr |
|
3 |
|
1stdm |
|
4 |
2 3
|
sylan |
|
5 |
|
eleq2 |
|
6 |
5
|
adantl |
|
7 |
6
|
adantr |
|
8 |
|
fvex |
|
9 |
|
eldm2g |
|
10 |
8 9
|
ax-mp |
|
11 |
|
simpr |
|
12 |
2
|
ad4antr |
|
13 |
|
1stdm |
|
14 |
12 13
|
sylancom |
|
15 |
|
eleq2 |
|
16 |
15
|
ad5antlr |
|
17 |
|
fvex |
|
18 |
|
eldm2g |
|
19 |
17 18
|
ax-mp |
|
20 |
|
simpr |
|
21 |
|
vex |
|
22 |
8 21
|
op1std |
|
23 |
22
|
eqcomd |
|
24 |
23
|
ad3antlr |
|
25 |
|
vex |
|
26 |
17 25
|
op1std |
|
27 |
26
|
eqcomd |
|
28 |
24 27
|
oveqan12d |
|
29 |
28
|
eqeq2d |
|
30 |
29
|
biimpd |
|
31 |
20 30
|
rspcimedv |
|
32 |
31
|
ex |
|
33 |
32
|
exlimdv |
|
34 |
19 33
|
syl5bi |
|
35 |
16 34
|
sylbid |
|
36 |
14 35
|
mpd |
|
37 |
36
|
rexlimdva |
|
38 |
|
eqidd |
|
39 |
38 23
|
goaleq12d |
|
40 |
39
|
eqeq2d |
|
41 |
40
|
biimpd |
|
42 |
41
|
adantl |
|
43 |
42
|
reximdv |
|
44 |
37 43
|
orim12d |
|
45 |
11 44
|
rspcimedv |
|
46 |
45
|
ex |
|
47 |
46
|
exlimdv |
|
48 |
10 47
|
syl5bi |
|
49 |
7 48
|
sylbid |
|
50 |
4 49
|
mpd |
|
51 |
50
|
rexlimdva |
|