Step |
Hyp |
Ref |
Expression |
1 |
|
satf0suc.s |
|
2 |
1
|
fveq1i |
|
3 |
2
|
a1i |
|
4 |
|
omsucelsucb |
|
5 |
|
satf0sucom |
|
6 |
4 5
|
sylbi |
|
7 |
|
nnon |
|
8 |
|
rdgsuc |
|
9 |
7 8
|
syl |
|
10 |
|
elelsuc |
|
11 |
|
satf0sucom |
|
12 |
10 11
|
syl |
|
13 |
1
|
eqcomi |
|
14 |
13
|
fveq1i |
|
15 |
12 14
|
eqtr3di |
|
16 |
15
|
fveq2d |
|
17 |
|
eqidd |
|
18 |
|
id |
|
19 |
|
rexeq |
|
20 |
19
|
orbi1d |
|
21 |
20
|
rexeqbi1dv |
|
22 |
21
|
anbi2d |
|
23 |
22
|
opabbidv |
|
24 |
18 23
|
uneq12d |
|
25 |
24
|
adantl |
|
26 |
|
fvex |
|
27 |
26
|
a1i |
|
28 |
|
omex |
|
29 |
|
satf0suclem |
|
30 |
26 26 28 29
|
mp3an |
|
31 |
26 30
|
unex |
|
32 |
31
|
a1i |
|
33 |
17 25 27 32
|
fvmptd |
|
34 |
9 16 33
|
3eqtrd |
|
35 |
3 6 34
|
3eqtrd |
|