Step |
Hyp |
Ref |
Expression |
1 |
|
dipdir.1 |
|
2 |
|
dipdir.2 |
|
3 |
|
dipdir.7 |
|
4 |
|
id |
|
5 |
4
|
3com13 |
|
6 |
|
id |
|
7 |
6
|
3com12 |
|
8 |
1 2 3
|
dipdir |
|
9 |
7 8
|
sylan2 |
|
10 |
9
|
fveq2d |
|
11 |
|
phnv |
|
12 |
|
simpl |
|
13 |
1 2
|
nvgcl |
|
14 |
13
|
3com23 |
|
15 |
14
|
3adant3r3 |
|
16 |
|
simpr3 |
|
17 |
1 3
|
dipcj |
|
18 |
12 15 16 17
|
syl3anc |
|
19 |
11 18
|
sylan |
|
20 |
1 3
|
dipcl |
|
21 |
20
|
3adant3r1 |
|
22 |
1 3
|
dipcl |
|
23 |
22
|
3adant3r2 |
|
24 |
21 23
|
cjaddd |
|
25 |
1 3
|
dipcj |
|
26 |
25
|
3adant3r1 |
|
27 |
1 3
|
dipcj |
|
28 |
27
|
3adant3r2 |
|
29 |
26 28
|
oveq12d |
|
30 |
24 29
|
eqtrd |
|
31 |
11 30
|
sylan |
|
32 |
10 19 31
|
3eqtr3d |
|
33 |
5 32
|
sylan2 |
|