Step |
Hyp |
Ref |
Expression |
1 |
|
sepnsepolem2.1 |
|
2 |
|
id |
|
3 |
2
|
sepnsepolem2 |
|
4 |
3
|
anbi2d |
|
5 |
4
|
rexbidv |
|
6 |
|
ssrin |
|
7 |
|
sseq0 |
|
8 |
7
|
ex |
|
9 |
6 8
|
syl |
|
10 |
9
|
adantl |
|
11 |
10
|
reximdv |
|
12 |
|
simpr |
|
13 |
12
|
ineq1d |
|
14 |
13
|
eqeq1d |
|
15 |
14
|
rexbidv |
|
16 |
2 11 15
|
opnneieqv |
|
17 |
|
sepnsepolem1 |
|
18 |
17
|
a1i |
|
19 |
5 16 18
|
3bitr4d |
|
20 |
1 19
|
syl |
|