Step |
Hyp |
Ref |
Expression |
1 |
|
prunioo |
|
2 |
1
|
eleq2d |
|
3 |
2
|
biimpar |
|
4 |
|
elun |
|
5 |
|
elprg |
|
6 |
5
|
orbi2d |
|
7 |
4 6
|
syl5bb |
|
8 |
7
|
adantl |
|
9 |
3 8
|
mpbid |
|
10 |
|
3orass |
|
11 |
|
3orcoma |
|
12 |
10 11
|
bitr3i |
|
13 |
9 12
|
sylib |
|
14 |
|
lbicc2 |
|
15 |
14
|
adantr |
|
16 |
|
eleq1 |
|
17 |
16
|
adantl |
|
18 |
15 17
|
mpbird |
|
19 |
|
ioossicc |
|
20 |
19
|
sseli |
|
21 |
20
|
adantl |
|
22 |
|
ubicc2 |
|
23 |
22
|
adantr |
|
24 |
|
eleq1 |
|
25 |
24
|
adantl |
|
26 |
23 25
|
mpbird |
|
27 |
18 21 26
|
3jaodan |
|
28 |
13 27
|
impbida |
|