Step |
Hyp |
Ref |
Expression |
1 |
|
sgn3da.0 |
|
2 |
|
sgn3da.1 |
|
3 |
|
sgn3da.2 |
|
4 |
|
sgn3da.3 |
|
5 |
|
sgn3da.4 |
|
6 |
|
sgn3da.5 |
|
7 |
|
sgn3da.6 |
|
8 |
|
sgnval |
|
9 |
1 8
|
syl |
|
10 |
9
|
eqeq2d |
|
11 |
10
|
pm5.32i |
|
12 |
2
|
eqcoms |
|
13 |
12
|
bicomd |
|
14 |
13
|
adantl |
|
15 |
11 14
|
sylbir |
|
16 |
15
|
expcom |
|
17 |
16
|
pm5.74d |
|
18 |
9
|
eqeq2d |
|
19 |
18
|
pm5.32i |
|
20 |
|
eqeq1 |
|
21 |
20
|
imbi1d |
|
22 |
|
eqeq1 |
|
23 |
22
|
imbi1d |
|
24 |
7
|
adantr |
|
25 |
|
simp2 |
|
26 |
25
|
3expia |
|
27 |
24 26
|
impbida |
|
28 |
|
pm3.24 |
|
29 |
28
|
pm2.21i |
|
30 |
29
|
adantl |
|
31 |
30
|
expr |
|
32 |
|
tbtru |
|
33 |
31 32
|
sylib |
|
34 |
27 33
|
anbi12d |
|
35 |
|
ancom |
|
36 |
|
truan |
|
37 |
35 36
|
bitri |
|
38 |
34 37
|
syl6bb |
|
39 |
38
|
3adant3 |
|
40 |
4
|
eqcoms |
|
41 |
40
|
3ad2ant3 |
|
42 |
39 41
|
bitr4d |
|
43 |
42
|
3expia |
|
44 |
7
|
3adant2 |
|
45 |
44
|
3expia |
|
46 |
|
tbtru |
|
47 |
45 46
|
sylib |
|
48 |
|
pm3.35 |
|
49 |
48
|
adantll |
|
50 |
|
simp2 |
|
51 |
50
|
3expia |
|
52 |
49 51
|
impbida |
|
53 |
47 52
|
anbi12d |
|
54 |
|
truan |
|
55 |
53 54
|
syl6bb |
|
56 |
55
|
3adant3 |
|
57 |
3
|
eqcoms |
|
58 |
57
|
3ad2ant3 |
|
59 |
56 58
|
bitr4d |
|
60 |
59
|
3expia |
|
61 |
21 23 43 60
|
ifbothda |
|
62 |
61
|
imp |
|
63 |
19 62
|
sylbir |
|
64 |
63
|
expcom |
|
65 |
64
|
pm5.74d |
|
66 |
5
|
expcom |
|
67 |
66
|
adantl |
|
68 |
7
|
ex |
|
69 |
68
|
adantr |
|
70 |
|
simp1 |
|
71 |
|
df-ne |
|
72 |
|
0xr |
|
73 |
|
xrlttri2 |
|
74 |
1 72 73
|
sylancl |
|
75 |
71 74
|
bitr3id |
|
76 |
75
|
biimpa |
|
77 |
76
|
ord |
|
78 |
77
|
3impia |
|
79 |
70 78 6
|
syl2anc |
|
80 |
79
|
3expia |
|
81 |
69 80
|
jca |
|
82 |
81
|
expcom |
|
83 |
82
|
adantl |
|
84 |
17 65 67 83
|
ifbothda |
|
85 |
84
|
mptru |
|