Step |
Hyp |
Ref |
Expression |
1 |
|
inss1 |
|
2 |
|
filsspw |
|
3 |
2
|
adantr |
|
4 |
1 3
|
sstrid |
|
5 |
|
0nelfil |
|
6 |
5
|
adantr |
|
7 |
|
elinel1 |
|
8 |
6 7
|
nsyl |
|
9 |
|
filtop |
|
10 |
9
|
adantr |
|
11 |
|
filtop |
|
12 |
11
|
adantl |
|
13 |
10 12
|
elind |
|
14 |
4 8 13
|
3jca |
|
15 |
|
simpll |
|
16 |
|
simpr2 |
|
17 |
|
elinel1 |
|
18 |
16 17
|
syl |
|
19 |
|
simpr1 |
|
20 |
19
|
elpwid |
|
21 |
|
simpr3 |
|
22 |
|
filss |
|
23 |
15 18 20 21 22
|
syl13anc |
|
24 |
|
simplr |
|
25 |
|
elinel2 |
|
26 |
16 25
|
syl |
|
27 |
|
filss |
|
28 |
24 26 20 21 27
|
syl13anc |
|
29 |
23 28
|
elind |
|
30 |
29
|
3exp2 |
|
31 |
30
|
imp |
|
32 |
31
|
rexlimdv |
|
33 |
32
|
ralrimiva |
|
34 |
|
simpl |
|
35 |
|
elinel1 |
|
36 |
35 17
|
anim12i |
|
37 |
|
filin |
|
38 |
37
|
3expb |
|
39 |
34 36 38
|
syl2an |
|
40 |
|
simpr |
|
41 |
|
elinel2 |
|
42 |
41 25
|
anim12i |
|
43 |
|
filin |
|
44 |
43
|
3expb |
|
45 |
40 42 44
|
syl2an |
|
46 |
39 45
|
elind |
|
47 |
46
|
ralrimivva |
|
48 |
|
isfil2 |
|
49 |
14 33 47 48
|
syl3anbrc |
|