Step |
Hyp |
Ref |
Expression |
1 |
|
3at.l |
|
2 |
|
3at.j |
|
3 |
|
3at.a |
|
4 |
1 2 3
|
3atlem7 |
|
5 |
4
|
3expia |
|
6 |
|
hllat |
|
7 |
|
simpl |
|
8 |
|
simpr1 |
|
9 |
|
eqid |
|
10 |
9 3
|
atbase |
|
11 |
8 10
|
syl |
|
12 |
|
simpr2 |
|
13 |
9 3
|
atbase |
|
14 |
12 13
|
syl |
|
15 |
9 2
|
latjcl |
|
16 |
7 11 14 15
|
syl3anc |
|
17 |
|
simpr3 |
|
18 |
9 3
|
atbase |
|
19 |
17 18
|
syl |
|
20 |
9 2
|
latjcl |
|
21 |
7 16 19 20
|
syl3anc |
|
22 |
9 1
|
latref |
|
23 |
21 22
|
syldan |
|
24 |
|
breq2 |
|
25 |
23 24
|
syl5ibcom |
|
26 |
6 25
|
sylan |
|
27 |
26
|
3adant3 |
|
28 |
27
|
adantr |
|
29 |
5 28
|
impbid |
|