Step |
Hyp |
Ref |
Expression |
1 |
|
trlval3.l |
|
2 |
|
trlval3.j |
|
3 |
|
trlval3.m |
|
4 |
|
trlval3.a |
|
5 |
|
trlval3.h |
|
6 |
|
trlval3.t |
|
7 |
|
trlval3.r |
|
8 |
|
simp1 |
|
9 |
|
simp21 |
|
10 |
|
simp22 |
|
11 |
|
simp23 |
|
12 |
|
simp3r |
|
13 |
|
simpl1l |
|
14 |
|
simp23l |
|
15 |
14
|
adantr |
|
16 |
|
simpl1 |
|
17 |
|
simpl21 |
|
18 |
1 4 5 6
|
ltrnat |
|
19 |
16 17 15 18
|
syl3anc |
|
20 |
1 2 4
|
hlatlej1 |
|
21 |
13 15 19 20
|
syl3anc |
|
22 |
|
simpl22 |
|
23 |
1 2 4 5 6 7
|
trljat1 |
|
24 |
16 17 22 23
|
syl3anc |
|
25 |
|
simpr |
|
26 |
24 25
|
eqtrd |
|
27 |
21 26
|
breqtrrd |
|
28 |
|
simpl3r |
|
29 |
|
simpll1 |
|
30 |
22
|
adantr |
|
31 |
17
|
adantr |
|
32 |
|
simpr |
|
33 |
|
eqid |
|
34 |
1 33 4 5 6 7
|
trl0 |
|
35 |
29 30 31 32 34
|
syl112anc |
|
36 |
|
hlatl |
|
37 |
13 36
|
syl |
|
38 |
|
simp22l |
|
39 |
38
|
adantr |
|
40 |
|
eqid |
|
41 |
40 2 4
|
hlatjcl |
|
42 |
13 39 15 41
|
syl3anc |
|
43 |
40 1 33
|
atl0le |
|
44 |
37 42 43
|
syl2anc |
|
45 |
44
|
adantr |
|
46 |
35 45
|
eqbrtrd |
|
47 |
46
|
ex |
|
48 |
47
|
necon3bd |
|
49 |
28 48
|
mpd |
|
50 |
1 4 5 6 7
|
trlat |
|
51 |
16 22 17 49 50
|
syl112anc |
|
52 |
|
simpl3l |
|
53 |
52
|
necomd |
|
54 |
1 2 4
|
hlatexch1 |
|
55 |
13 15 51 39 53 54
|
syl131anc |
|
56 |
27 55
|
mpd |
|
57 |
56
|
ex |
|
58 |
57
|
necon3bd |
|
59 |
12 58
|
mpd |
|
60 |
1 2 3 4 5 6 7
|
trlval3 |
|
61 |
8 9 10 11 59 60
|
syl113anc |
|