Step |
Hyp |
Ref |
Expression |
1 |
|
sge0ltfirp.x |
|
2 |
|
sge0ltfirp.f |
|
3 |
|
sge0ltfirp.y |
|
4 |
|
sge0ltfirp.re |
|
5 |
1 2 4
|
sge0rern |
|
6 |
2 5
|
fge0iccico |
|
7 |
6
|
sge0rnre |
|
8 |
|
sge0rnn0 |
|
9 |
8
|
a1i |
|
10 |
1 2 4
|
sge0rnbnd |
|
11 |
7 9 10 3
|
suprltrp |
|
12 |
|
nfv |
|
13 |
|
nfv |
|
14 |
|
simp1 |
|
15 |
|
vex |
|
16 |
|
eqid |
|
17 |
16
|
elrnmpt |
|
18 |
15 17
|
ax-mp |
|
19 |
18
|
biimpi |
|
20 |
19
|
adantr |
|
21 |
|
nfmpt1 |
|
22 |
21
|
nfrn |
|
23 |
|
nfcv |
|
24 |
|
nfcv |
|
25 |
22 23 24
|
nfsup |
|
26 |
|
nfcv |
|
27 |
|
nfcv |
|
28 |
25 26 27
|
nfov |
|
29 |
|
nfcv |
|
30 |
28 24 29
|
nfbr |
|
31 |
|
simpl |
|
32 |
|
simpr |
|
33 |
31 32
|
breqtrd |
|
34 |
33
|
ex |
|
35 |
34
|
a1d |
|
36 |
30 35
|
reximdai |
|
37 |
36
|
adantl |
|
38 |
20 37
|
mpd |
|
39 |
38
|
3adant1 |
|
40 |
|
simpl |
|
41 |
1 2 4
|
sge0supre |
|
42 |
41
|
oveq1d |
|
43 |
42
|
adantr |
|
44 |
|
simpr |
|
45 |
43 44
|
eqbrtrd |
|
46 |
45
|
adantlr |
|
47 |
|
simpr |
|
48 |
4
|
adantr |
|
49 |
3
|
rpred |
|
50 |
49
|
adantr |
|
51 |
|
elinel2 |
|
52 |
51
|
adantl |
|
53 |
|
rge0ssre |
|
54 |
6
|
adantr |
|
55 |
54
|
adantr |
|
56 |
|
elpwinss |
|
57 |
56
|
adantl |
|
58 |
57
|
sselda |
|
59 |
55 58
|
ffvelrnd |
|
60 |
53 59
|
sseldi |
|
61 |
52 60
|
fsumrecl |
|
62 |
48 50 61
|
ltsubaddd |
|
63 |
62
|
adantr |
|
64 |
47 63
|
mpbid |
|
65 |
54 57
|
fssresd |
|
66 |
52 65
|
sge0fsum |
|
67 |
|
fvres |
|
68 |
67
|
sumeq2i |
|
69 |
68
|
a1i |
|
70 |
66 69
|
eqtr2d |
|
71 |
70
|
oveq1d |
|
72 |
71
|
adantr |
|
73 |
64 72
|
breqtrd |
|
74 |
40 46 73
|
syl2anc |
|
75 |
74
|
ex |
|
76 |
75
|
reximdva |
|
77 |
76
|
imp |
|
78 |
14 39 77
|
syl2anc |
|
79 |
78
|
3exp |
|
80 |
12 13 79
|
rexlimd |
|
81 |
11 80
|
mpd |
|