Step |
Hyp |
Ref |
Expression |
1 |
|
iccssxr |
|
2 |
|
simpl1 |
|
3 |
1 2
|
sseldi |
|
4 |
|
simpr |
|
5 |
|
simpl3 |
|
6 |
4 5
|
eqbrtrrd |
|
7 |
|
xgepnf |
|
8 |
7
|
biimpa |
|
9 |
3 6 8
|
syl2anc |
|
10 |
|
xnegeq |
|
11 |
4 10
|
syl |
|
12 |
9 11
|
oveq12d |
|
13 |
|
pnfxr |
|
14 |
|
xnegid |
|
15 |
13 14
|
ax-mp |
|
16 |
12 15
|
eqtrdi |
|
17 |
16
|
oveq1d |
|
18 |
4
|
oveq2d |
|
19 |
|
xaddid2 |
|
20 |
13 19
|
mp1i |
|
21 |
17 18 20
|
3eqtrd |
|
22 |
21 9
|
eqtr4d |
|
23 |
|
simpl1 |
|
24 |
1 23
|
sseldi |
|
25 |
|
xrge0neqmnf |
|
26 |
23 25
|
syl |
|
27 |
|
simpl2 |
|
28 |
1 27
|
sseldi |
|
29 |
28
|
xnegcld |
|
30 |
|
simpr |
|
31 |
|
xnegneg |
|
32 |
|
xnegeq |
|
33 |
31 32
|
sylan9req |
|
34 |
|
xnegmnf |
|
35 |
33 34
|
eqtrdi |
|
36 |
35
|
stoic1a |
|
37 |
36
|
neqned |
|
38 |
28 30 37
|
syl2anc |
|
39 |
|
xrge0neqmnf |
|
40 |
27 39
|
syl |
|
41 |
|
xaddass |
|
42 |
24 26 29 38 28 40 41
|
syl222anc |
|
43 |
|
xnegcl |
|
44 |
|
xaddcom |
|
45 |
43 44
|
mpancom |
|
46 |
|
xnegid |
|
47 |
45 46
|
eqtrd |
|
48 |
47
|
oveq2d |
|
49 |
|
xaddid1 |
|
50 |
48 49
|
sylan9eqr |
|
51 |
24 28 50
|
syl2anc |
|
52 |
42 51
|
eqtrd |
|
53 |
22 52
|
pm2.61dan |
|