Step |
Hyp |
Ref |
Expression |
1 |
|
sge0lefi.1 |
|
2 |
|
sge0lefi.2 |
|
3 |
|
sge0lefi.3 |
|
4 |
|
simpr |
|
5 |
2
|
adantr |
|
6 |
|
elpwinss |
|
7 |
6
|
adantl |
|
8 |
5 7
|
fssresd |
|
9 |
4 8
|
sge0xrcl |
|
10 |
9
|
adantlr |
|
11 |
1 2
|
sge0xrcl |
|
12 |
11
|
ad2antrr |
|
13 |
3
|
ad2antrr |
|
14 |
1
|
adantr |
|
15 |
14 5
|
sge0less |
|
16 |
15
|
adantlr |
|
17 |
|
simplr |
|
18 |
10 12 13 16 17
|
xrletrd |
|
19 |
18
|
ralrimiva |
|
20 |
19
|
ex |
|
21 |
1 2
|
sge0sup |
|
22 |
21
|
adantr |
|
23 |
|
vex |
|
24 |
|
eqid |
|
25 |
24
|
elrnmpt |
|
26 |
23 25
|
ax-mp |
|
27 |
26
|
biimpi |
|
28 |
27
|
adantl |
|
29 |
|
nfv |
|
30 |
|
nfra1 |
|
31 |
29 30
|
nfan |
|
32 |
|
nfcv |
|
33 |
|
nfmpt1 |
|
34 |
33
|
nfrn |
|
35 |
32 34
|
nfel |
|
36 |
31 35
|
nfan |
|
37 |
|
nfv |
|
38 |
|
simp3 |
|
39 |
|
rspa |
|
40 |
39
|
3adant3 |
|
41 |
38 40
|
eqbrtrd |
|
42 |
41
|
3adant1l |
|
43 |
42
|
3exp |
|
44 |
43
|
adantr |
|
45 |
36 37 44
|
rexlimd |
|
46 |
28 45
|
mpd |
|
47 |
46
|
ralrimiva |
|
48 |
9
|
ralrimiva |
|
49 |
24
|
rnmptss |
|
50 |
48 49
|
syl |
|
51 |
50
|
adantr |
|
52 |
3
|
adantr |
|
53 |
|
supxrleub |
|
54 |
51 52 53
|
syl2anc |
|
55 |
47 54
|
mpbird |
|
56 |
22 55
|
eqbrtrd |
|
57 |
56
|
ex |
|
58 |
20 57
|
impbid |
|