Step |
Hyp |
Ref |
Expression |
1 |
|
hlatexch4.j |
|
2 |
|
hlatexch4.a |
|
3 |
|
simp1 |
|
4 |
|
simp21 |
|
5 |
|
simp22 |
|
6 |
|
eqid |
|
7 |
6 1 2
|
hlatlej2 |
|
8 |
3 4 5 7
|
syl3anc |
|
9 |
|
simp23 |
|
10 |
6 1 2
|
hlatlej2 |
|
11 |
3 4 9 10
|
syl3anc |
|
12 |
|
simp3r |
|
13 |
11 12
|
breqtrrd |
|
14 |
|
hllat |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
eqid |
|
17 |
16 2
|
atbase |
|
18 |
5 17
|
syl |
|
19 |
16 2
|
atbase |
|
20 |
9 19
|
syl |
|
21 |
16 1 2
|
hlatjcl |
|
22 |
3 4 5 21
|
syl3anc |
|
23 |
16 6 1
|
latjle12 |
|
24 |
15 18 20 22 23
|
syl13anc |
|
25 |
8 13 24
|
mpbi2and |
|
26 |
|
simp3l |
|
27 |
6 1 2
|
ps-1 |
|
28 |
3 5 9 26 4 5 27
|
syl132anc |
|
29 |
25 28
|
mpbid |
|
30 |
29
|
eqcomd |
|