Step |
Hyp |
Ref |
Expression |
1 |
|
ps1.l |
|
2 |
|
ps1.j |
|
3 |
|
ps1.a |
|
4 |
|
oveq1 |
|
5 |
4
|
breq2d |
|
6 |
4
|
eqeq2d |
|
7 |
5 6
|
imbi12d |
|
8 |
7
|
eqcoms |
|
9 |
|
simp3 |
|
10 |
|
simp1 |
|
11 |
|
simp21 |
|
12 |
|
simp3l |
|
13 |
2 3
|
hlatjcom |
|
14 |
10 11 12 13
|
syl3anc |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
hllat |
|
17 |
16
|
3ad2ant1 |
|
18 |
|
eqid |
|
19 |
18 3
|
atbase |
|
20 |
11 19
|
syl |
|
21 |
|
simp22 |
|
22 |
18 3
|
atbase |
|
23 |
21 22
|
syl |
|
24 |
|
simp3r |
|
25 |
18 2 3
|
hlatjcl |
|
26 |
10 12 24 25
|
syl3anc |
|
27 |
18 1 2
|
latjle12 |
|
28 |
17 20 23 26 27
|
syl13anc |
|
29 |
|
simpl |
|
30 |
28 29
|
syl6bir |
|
31 |
30
|
adantr |
|
32 |
|
simpl1 |
|
33 |
|
simpl21 |
|
34 |
|
simpl3r |
|
35 |
|
simpl3l |
|
36 |
|
simpr |
|
37 |
1 2 3
|
hlatexchb1 |
|
38 |
32 33 34 35 36 37
|
syl131anc |
|
39 |
31 38
|
sylibd |
|
40 |
39
|
3impia |
|
41 |
15 40
|
eqtrd |
|
42 |
9 41
|
breqtrrd |
|
43 |
42
|
3expia |
|
44 |
18 2 3
|
hlatjcl |
|
45 |
10 11 12 44
|
syl3anc |
|
46 |
18 1 2
|
latjle12 |
|
47 |
17 20 23 45 46
|
syl13anc |
|
48 |
|
simpr |
|
49 |
|
simp23 |
|
50 |
49
|
necomd |
|
51 |
1 2 3
|
hlatexchb1 |
|
52 |
10 21 12 11 50 51
|
syl131anc |
|
53 |
48 52
|
syl5ib |
|
54 |
47 53
|
sylbird |
|
55 |
54
|
adantr |
|
56 |
43 55
|
syld |
|
57 |
56
|
3impia |
|
58 |
57 41
|
eqtrd |
|
59 |
58
|
3expia |
|
60 |
18 2 3
|
hlatjcl |
|
61 |
10 11 24 60
|
syl3anc |
|
62 |
18 1 2
|
latjle12 |
|
63 |
17 20 23 61 62
|
syl13anc |
|
64 |
|
simpr |
|
65 |
63 64
|
syl6bir |
|
66 |
1 2 3
|
hlatexchb1 |
|
67 |
10 21 24 11 50 66
|
syl131anc |
|
68 |
65 67
|
sylibd |
|
69 |
8 59 68
|
pm2.61ne |
|
70 |
18 2 3
|
hlatjcl |
|
71 |
10 11 21 70
|
syl3anc |
|
72 |
18 1
|
latref |
|
73 |
17 71 72
|
syl2anc |
|
74 |
|
breq2 |
|
75 |
73 74
|
syl5ibcom |
|
76 |
69 75
|
impbid |
|