Step |
Hyp |
Ref |
Expression |
1 |
|
0re |
|
2 |
|
lttri4 |
|
3 |
1 2
|
mpan2 |
|
4 |
|
reneg1lt0 |
|
5 |
|
1re |
|
6 |
|
rernegcl |
|
7 |
5 6
|
ax-mp |
|
8 |
7 1
|
ltnsymi |
|
9 |
4 8
|
ax-mp |
|
10 |
|
relt0neg1 |
|
11 |
|
rernegcl |
|
12 |
|
mulgt0 |
|
13 |
12
|
anidms |
|
14 |
11 13
|
sylan |
|
15 |
|
elre0re |
|
16 |
|
id |
|
17 |
|
resubdi |
|
18 |
11 15 16 17
|
syl3anc |
|
19 |
|
remul01 |
|
20 |
11 19
|
syl |
|
21 |
16 16
|
remulcld |
|
22 |
16 21
|
remulcld |
|
23 |
|
ipiiie0 |
|
24 |
|
renegadd |
|
25 |
23 24
|
mpbiri |
|
26 |
22 25
|
mpdan |
|
27 |
26
|
oveq1d |
|
28 |
|
ax-icn |
|
29 |
28 28 28
|
mulassi |
|
30 |
29
|
oveq1i |
|
31 |
28 28
|
mulcli |
|
32 |
31 28 28
|
mulassi |
|
33 |
30 32
|
eqtr3i |
|
34 |
33
|
a1i |
|
35 |
|
rei4 |
|
36 |
35
|
a1i |
|
37 |
27 34 36
|
3eqtrd |
|
38 |
20 37
|
oveq12d |
|
39 |
18 38
|
eqtrd |
|
40 |
39
|
breq2d |
|
41 |
40
|
adantr |
|
42 |
14 41
|
mpbid |
|
43 |
42
|
ex |
|
44 |
10 43
|
sylbid |
|
45 |
9 44
|
mtoi |
|
46 |
|
0ne1 |
|
47 |
46
|
neii |
|
48 |
|
oveq12 |
|
49 |
48
|
anidms |
|
50 |
49
|
oveq1d |
|
51 |
|
ax-i2m1 |
|
52 |
|
remul02 |
|
53 |
1 52
|
ax-mp |
|
54 |
53
|
oveq1i |
|
55 |
|
readdid2 |
|
56 |
5 55
|
ax-mp |
|
57 |
54 56
|
eqtri |
|
58 |
50 51 57
|
3eqtr3g |
|
59 |
47 58
|
mto |
|
60 |
59
|
a1i |
|
61 |
|
mulgt0 |
|
62 |
61
|
anidms |
|
63 |
|
reixi |
|
64 |
62 63
|
breqtrdi |
|
65 |
64
|
ex |
|
66 |
9 65
|
mtoi |
|
67 |
|
3ioran |
|
68 |
45 60 66 67
|
syl3anbrc |
|
69 |
3 68
|
pm2.65i |
|