Step |
Hyp |
Ref |
Expression |
1 |
|
elxr |
|
2 |
|
simpll |
|
3 |
2
|
rexrd |
|
4 |
|
xnegneg |
|
5 |
3 4
|
syl |
|
6 |
3
|
xnegcld |
|
7 |
|
xaddid2 |
|
8 |
6 7
|
syl |
|
9 |
|
simplr |
|
10 |
|
xaddcom |
|
11 |
3 9 10
|
syl2anc |
|
12 |
11
|
oveq1d |
|
13 |
|
simpr |
|
14 |
13
|
oveq1d |
|
15 |
|
xpncan |
|
16 |
15
|
ancoms |
|
17 |
16
|
adantr |
|
18 |
12 14 17
|
3eqtr3d |
|
19 |
8 18
|
eqtr3d |
|
20 |
|
xnegeq |
|
21 |
19 20
|
syl |
|
22 |
5 21
|
eqtr3d |
|
23 |
22
|
ex |
|
24 |
|
simpll |
|
25 |
|
simplr |
|
26 |
24
|
oveq1d |
|
27 |
|
simpr |
|
28 |
26 27
|
eqtr3d |
|
29 |
|
0re |
|
30 |
|
renepnf |
|
31 |
29 30
|
mp1i |
|
32 |
28 31
|
eqnetrd |
|
33 |
32
|
neneqd |
|
34 |
|
xaddpnf2 |
|
35 |
34
|
stoic1a |
|
36 |
25 33 35
|
syl2anc |
|
37 |
|
nne |
|
38 |
36 37
|
sylib |
|
39 |
|
xnegeq |
|
40 |
38 39
|
syl |
|
41 |
|
xnegmnf |
|
42 |
40 41
|
eqtr2di |
|
43 |
24 42
|
eqtrd |
|
44 |
43
|
ex |
|
45 |
|
simpll |
|
46 |
|
simplr |
|
47 |
45
|
oveq1d |
|
48 |
|
simpr |
|
49 |
47 48
|
eqtr3d |
|
50 |
|
renemnf |
|
51 |
29 50
|
mp1i |
|
52 |
49 51
|
eqnetrd |
|
53 |
52
|
neneqd |
|
54 |
|
xaddmnf2 |
|
55 |
54
|
stoic1a |
|
56 |
46 53 55
|
syl2anc |
|
57 |
|
nne |
|
58 |
56 57
|
sylib |
|
59 |
|
xnegeq |
|
60 |
58 59
|
syl |
|
61 |
|
xnegpnf |
|
62 |
60 61
|
eqtr2di |
|
63 |
45 62
|
eqtrd |
|
64 |
63
|
ex |
|
65 |
23 44 64
|
3jaoian |
|
66 |
1 65
|
sylanb |
|
67 |
|
simpr |
|
68 |
67
|
oveq1d |
|
69 |
|
xnegcl |
|
70 |
69
|
ad2antlr |
|
71 |
|
simplr |
|
72 |
|
xaddcom |
|
73 |
70 71 72
|
syl2anc |
|
74 |
|
xnegid |
|
75 |
74
|
ad2antlr |
|
76 |
68 73 75
|
3eqtrd |
|
77 |
76
|
ex |
|
78 |
66 77
|
impbid |
|