Step |
Hyp |
Ref |
Expression |
1 |
|
2atmat.l |
|
2 |
|
2atmat.j |
|
3 |
|
2atmat.m |
|
4 |
|
2atmat.a |
|
5 |
|
simp11 |
|
6 |
5
|
hllatd |
|
7 |
|
eqid |
|
8 |
7 2 4
|
hlatjcl |
|
9 |
8
|
3ad2ant1 |
|
10 |
|
simp21 |
|
11 |
7 4
|
atbase |
|
12 |
10 11
|
syl |
|
13 |
|
simp22 |
|
14 |
7 4
|
atbase |
|
15 |
13 14
|
syl |
|
16 |
7 2
|
latjass |
|
17 |
6 9 12 15 16
|
syl13anc |
|
18 |
|
simp33 |
|
19 |
7 2
|
latjcl |
|
20 |
6 9 12 19
|
syl3anc |
|
21 |
7 1 2
|
latleeqj2 |
|
22 |
6 15 20 21
|
syl3anc |
|
23 |
18 22
|
mpbid |
|
24 |
17 23
|
eqtr3d |
|
25 |
|
simp23 |
|
26 |
|
simp32 |
|
27 |
|
simp12 |
|
28 |
|
simp13 |
|
29 |
|
eqid |
|
30 |
1 2 4 29
|
islpln2a |
|
31 |
5 27 28 10 30
|
syl13anc |
|
32 |
25 26 31
|
mpbir2and |
|
33 |
24 32
|
eqeltrd |
|
34 |
|
eqid |
|
35 |
2 4 34
|
llni2 |
|
36 |
5 27 28 25 35
|
syl31anc |
|
37 |
|
simp31 |
|
38 |
2 4 34
|
llni2 |
|
39 |
5 10 13 37 38
|
syl31anc |
|
40 |
2 3 4 34 29
|
2llnmj |
|
41 |
5 36 39 40
|
syl3anc |
|
42 |
33 41
|
mpbird |
|