Step |
Hyp |
Ref |
Expression |
1 |
|
3oalem1.1 |
|
2 |
|
3oalem1.2 |
|
3 |
|
3oalem1.3 |
|
4 |
|
3oalem1.4 |
|
5 |
|
simplll |
|
6 |
|
simpllr |
|
7 |
1 2 3 4
|
3oalem1 |
|
8 |
|
hvaddsub12 |
|
9 |
8
|
3anidm23 |
|
10 |
|
hvsubid |
|
11 |
10
|
oveq2d |
|
12 |
|
ax-hvaddid |
|
13 |
11 12
|
sylan9eqr |
|
14 |
9 13
|
eqtr3d |
|
15 |
14
|
ad2ant2l |
|
16 |
15
|
adantlr |
|
17 |
7 16
|
syl |
|
18 |
|
simprlr |
|
19 |
|
eqtr2 |
|
20 |
19
|
oveq1d |
|
21 |
20
|
ad2ant2l |
|
22 |
|
simpl |
|
23 |
22
|
anim1i |
|
24 |
|
hvsub4 |
|
25 |
23 24
|
syldan |
|
26 |
|
hvsubid |
|
27 |
26
|
ad2antrr |
|
28 |
27
|
oveq1d |
|
29 |
|
hvsubcl |
|
30 |
|
hvaddid2 |
|
31 |
29 30
|
syl |
|
32 |
31
|
adantll |
|
33 |
25 28 32
|
3eqtrd |
|
34 |
33
|
ad2ant2rl |
|
35 |
7 34
|
syl |
|
36 |
|
simpr |
|
37 |
|
simpr |
|
38 |
37
|
anim2i |
|
39 |
|
hvsub4 |
|
40 |
36 38 39
|
syl2anc |
|
41 |
10
|
ad2antll |
|
42 |
41
|
oveq2d |
|
43 |
|
hvsubcl |
|
44 |
|
ax-hvaddid |
|
45 |
43 44
|
syl |
|
46 |
45
|
ancoms |
|
47 |
46
|
adantrr |
|
48 |
40 42 47
|
3eqtrd |
|
49 |
48
|
adantlr |
|
50 |
49
|
adantlr |
|
51 |
7 50
|
syl |
|
52 |
21 35 51
|
3eqtr3d |
|
53 |
|
simpll |
|
54 |
|
simpll |
|
55 |
2
|
chshii |
|
56 |
1
|
chshii |
|
57 |
55 56
|
shsvsi |
|
58 |
57
|
ancoms |
|
59 |
56 55
|
shscomi |
|
60 |
58 59
|
eleqtrrdi |
|
61 |
53 54 60
|
syl2an |
|
62 |
52 61
|
eqeltrd |
|
63 |
|
simplr |
|
64 |
|
simplr |
|
65 |
3
|
chshii |
|
66 |
4
|
chshii |
|
67 |
65 66
|
shsvsi |
|
68 |
63 64 67
|
syl2an |
|
69 |
62 68
|
elind |
|
70 |
56 55
|
shscli |
|
71 |
65 66
|
shscli |
|
72 |
70 71
|
shincli |
|
73 |
66 72
|
shsvai |
|
74 |
18 69 73
|
syl2anc |
|
75 |
17 74
|
eqeltrrd |
|
76 |
6 75
|
elind |
|
77 |
66 72
|
shscli |
|
78 |
65 77
|
shincli |
|
79 |
56 78
|
shsvai |
|
80 |
5 76 79
|
syl2anc |
|
81 |
|
eleq1 |
|
82 |
81
|
ad2antlr |
|
83 |
80 82
|
mpbird |
|