Step |
Hyp |
Ref |
Expression |
1 |
|
signsw.p |
|
2 |
|
signsw.w |
|
3 |
|
df-pr |
|
4 |
|
snsstp1 |
|
5 |
|
snsstp3 |
|
6 |
4 5
|
unssi |
|
7 |
3 6
|
eqsstri |
|
8 |
7
|
sseli |
|
9 |
1
|
signspval |
|
10 |
8 9
|
sylan |
|
11 |
10
|
neeq1d |
|
12 |
|
neeq1 |
|
13 |
12
|
bibi1d |
|
14 |
|
neeq1 |
|
15 |
14
|
bibi1d |
|
16 |
|
neirr |
|
17 |
16
|
a1i |
|
18 |
|
0re |
|
19 |
18
|
ltnri |
|
20 |
|
simpr |
|
21 |
20
|
oveq2d |
|
22 |
|
neg1cn |
|
23 |
|
ax-1cn |
|
24 |
|
prssi |
|
25 |
22 23 24
|
mp2an |
|
26 |
|
simpll |
|
27 |
25 26
|
sseldi |
|
28 |
27
|
mul01d |
|
29 |
21 28
|
eqtrd |
|
30 |
29
|
breq1d |
|
31 |
19 30
|
mtbiri |
|
32 |
17 31
|
2falsed |
|
33 |
|
simplr |
|
34 |
|
tpcomb |
|
35 |
33 34
|
eleqtrdi |
|
36 |
|
simpr |
|
37 |
36
|
neqned |
|
38 |
35 37
|
jca |
|
39 |
|
eldifsn |
|
40 |
|
neg1ne0 |
|
41 |
|
ax-1ne0 |
|
42 |
|
diftpsn3 |
|
43 |
40 41 42
|
mp2an |
|
44 |
43
|
eleq2i |
|
45 |
39 44
|
bitr3i |
|
46 |
38 45
|
sylib |
|
47 |
|
neirr |
|
48 |
|
0le1 |
|
49 |
|
1re |
|
50 |
18 49
|
lenlti |
|
51 |
48 50
|
mpbi |
|
52 |
|
neg1mulneg1e1 |
|
53 |
52
|
breq1i |
|
54 |
51 53
|
mtbir |
|
55 |
47 54
|
2false |
|
56 |
|
neeq1 |
|
57 |
|
oveq2 |
|
58 |
57
|
breq1d |
|
59 |
56 58
|
bibi12d |
|
60 |
55 59
|
mpbiri |
|
61 |
60
|
adantl |
|
62 |
|
neg1rr |
|
63 |
|
neg1lt0 |
|
64 |
|
0lt1 |
|
65 |
62 18 49
|
lttri |
|
66 |
63 64 65
|
mp2an |
|
67 |
62 66
|
gtneii |
|
68 |
22
|
mulid1i |
|
69 |
68 63
|
eqbrtri |
|
70 |
67 69
|
2th |
|
71 |
|
neeq1 |
|
72 |
|
oveq2 |
|
73 |
72
|
breq1d |
|
74 |
71 73
|
bibi12d |
|
75 |
70 74
|
mpbiri |
|
76 |
75
|
adantl |
|
77 |
|
elpri |
|
78 |
61 76 77
|
mpjaodan |
|
79 |
78
|
adantr |
|
80 |
|
neeq2 |
|
81 |
|
oveq1 |
|
82 |
81
|
breq1d |
|
83 |
80 82
|
bibi12d |
|
84 |
83
|
adantl |
|
85 |
79 84
|
mpbird |
|
86 |
46 85
|
sylan |
|
87 |
67
|
necomi |
|
88 |
22 23
|
mulcomi |
|
89 |
88
|
breq1i |
|
90 |
69 89
|
mpbi |
|
91 |
87 90
|
2th |
|
92 |
|
neeq1 |
|
93 |
|
oveq2 |
|
94 |
93
|
breq1d |
|
95 |
92 94
|
bibi12d |
|
96 |
91 95
|
mpbiri |
|
97 |
96
|
adantl |
|
98 |
|
neirr |
|
99 |
23
|
mulid1i |
|
100 |
99
|
breq1i |
|
101 |
51 100
|
mtbir |
|
102 |
98 101
|
2false |
|
103 |
|
neeq1 |
|
104 |
|
oveq2 |
|
105 |
104
|
breq1d |
|
106 |
103 105
|
bibi12d |
|
107 |
102 106
|
mpbiri |
|
108 |
107
|
adantl |
|
109 |
97 108 77
|
mpjaodan |
|
110 |
109
|
adantr |
|
111 |
|
neeq2 |
|
112 |
|
oveq1 |
|
113 |
112
|
breq1d |
|
114 |
111 113
|
bibi12d |
|
115 |
114
|
adantl |
|
116 |
110 115
|
mpbird |
|
117 |
46 116
|
sylan |
|
118 |
|
elpri |
|
119 |
118
|
ad2antrr |
|
120 |
86 117 119
|
mpjaodan |
|
121 |
13 15 32 120
|
ifbothda |
|
122 |
11 121
|
bitrd |
|