Step |
Hyp |
Ref |
Expression |
1 |
|
chincl |
|
2 |
|
chincl |
|
3 |
|
chjcl |
|
4 |
1 2 3
|
syl2an |
|
5 |
4
|
anandis |
|
6 |
|
chjcl |
|
7 |
|
chincl |
|
8 |
6 7
|
sylan2 |
|
9 |
|
chsh |
|
10 |
8 9
|
syl |
|
11 |
5 10
|
jca |
|
12 |
11
|
3impb |
|
13 |
12
|
adantr |
|
14 |
|
ledi |
|
15 |
14
|
adantr |
|
16 |
|
incom |
|
17 |
16
|
a1i |
|
18 |
|
chdmj1 |
|
19 |
1 2 18
|
syl2an |
|
20 |
|
chdmm1 |
|
21 |
|
chdmm1 |
|
22 |
20 21
|
ineqan12d |
|
23 |
19 22
|
eqtrd |
|
24 |
17 23
|
ineq12d |
|
25 |
24
|
3impdi |
|
26 |
25
|
adantr |
|
27 |
|
inass |
|
28 |
|
cmcm2 |
|
29 |
|
choccl |
|
30 |
|
cmbr3 |
|
31 |
29 30
|
sylan2 |
|
32 |
28 31
|
bitrd |
|
33 |
32
|
biimpa |
|
34 |
33
|
3adantl3 |
|
35 |
34
|
adantrr |
|
36 |
|
cmcm2 |
|
37 |
|
choccl |
|
38 |
|
cmbr3 |
|
39 |
37 38
|
sylan2 |
|
40 |
36 39
|
bitrd |
|
41 |
40
|
biimpa |
|
42 |
41
|
3adantl2 |
|
43 |
42
|
adantrl |
|
44 |
35 43
|
ineq12d |
|
45 |
|
inindi |
|
46 |
|
inindi |
|
47 |
44 45 46
|
3eqtr4g |
|
48 |
47
|
ineq2d |
|
49 |
27 48
|
syl5eq |
|
50 |
|
in12 |
|
51 |
49 50
|
eqtrdi |
|
52 |
|
chdmj1 |
|
53 |
52
|
ineq2d |
|
54 |
|
chocin |
|
55 |
6 54
|
syl |
|
56 |
53 55
|
eqtr3d |
|
57 |
56
|
ineq2d |
|
58 |
|
chm0 |
|
59 |
57 58
|
sylan9eqr |
|
60 |
59
|
3impb |
|
61 |
60
|
adantr |
|
62 |
51 61
|
eqtrd |
|
63 |
26 62
|
eqtrd |
|
64 |
|
pjoml |
|
65 |
13 15 63 64
|
syl12anc |
|
66 |
65
|
eqcomd |
|