Step |
Hyp |
Ref |
Expression |
1 |
|
4at.l |
|
2 |
|
4at.j |
|
3 |
|
4at.a |
|
4 |
|
simp11 |
|
5 |
|
simp121 |
|
6 |
|
simp122 |
|
7 |
5 6
|
jca |
|
8 |
|
simp13 |
|
9 |
4 7 8
|
3jca |
|
10 |
|
simp2l |
|
11 |
9 10
|
jca |
|
12 |
|
simp3lr |
|
13 |
|
simp3rl |
|
14 |
|
simp3rr |
|
15 |
|
simp111 |
|
16 |
15
|
hllatd |
|
17 |
|
eqid |
|
18 |
17 3
|
atbase |
|
19 |
5 18
|
syl |
|
20 |
17 3
|
atbase |
|
21 |
6 20
|
syl |
|
22 |
|
simp123 |
|
23 |
|
simp131 |
|
24 |
17 2 3
|
hlatjcl |
|
25 |
15 22 23 24
|
syl3anc |
|
26 |
|
simp132 |
|
27 |
|
simp133 |
|
28 |
17 2 3
|
hlatjcl |
|
29 |
15 26 27 28
|
syl3anc |
|
30 |
17 2
|
latjcl |
|
31 |
16 25 29 30
|
syl3anc |
|
32 |
17 1 2
|
latjle12 |
|
33 |
16 19 21 31 32
|
syl13anc |
|
34 |
13 14 33
|
mpbi2and |
|
35 |
|
simp113 |
|
36 |
17 3
|
atbase |
|
37 |
35 36
|
syl |
|
38 |
17 2 3
|
hlatjcl |
|
39 |
15 5 6 38
|
syl3anc |
|
40 |
17 1 2
|
latjle12 |
|
41 |
16 37 39 31 40
|
syl13anc |
|
42 |
12 34 41
|
mpbi2and |
|
43 |
|
simp3ll |
|
44 |
|
simp112 |
|
45 |
|
simp2r |
|
46 |
1 2 3
|
4atlem12a |
|
47 |
15 44 22 8 45 46
|
syl311anc |
|
48 |
43 47
|
mpbid |
|
49 |
42 48
|
breqtrrd |
|
50 |
1 2 3
|
4atlem11 |
|
51 |
11 49 50
|
sylc |
|
52 |
51 48
|
eqtrd |
|