Step |
Hyp |
Ref |
Expression |
1 |
|
satfsschain.s |
|
2 |
|
fveq2 |
|
3 |
2
|
sseq2d |
|
4 |
3
|
imbi2d |
|
5 |
|
fveq2 |
|
6 |
5
|
sseq2d |
|
7 |
6
|
imbi2d |
|
8 |
|
fveq2 |
|
9 |
8
|
sseq2d |
|
10 |
9
|
imbi2d |
|
11 |
|
fveq2 |
|
12 |
11
|
sseq2d |
|
13 |
12
|
imbi2d |
|
14 |
|
ssidd |
|
15 |
14
|
a1i |
|
16 |
|
pm2.27 |
|
17 |
16
|
adantl |
|
18 |
|
simpr |
|
19 |
|
ssun1 |
|
20 |
|
simpl |
|
21 |
|
simpr |
|
22 |
|
simplll |
|
23 |
1
|
satfvsuc |
|
24 |
20 21 22 23
|
syl2an23an |
|
25 |
19 24
|
sseqtrrid |
|
26 |
25
|
adantr |
|
27 |
18 26
|
sstrd |
|
28 |
27
|
ex |
|
29 |
17 28
|
syld |
|
30 |
29
|
ex |
|
31 |
30
|
com23 |
|
32 |
4 7 10 13 15 31
|
findsg |
|
33 |
32
|
ex |
|
34 |
33
|
com23 |
|
35 |
34
|
impcom |
|