Step |
Hyp |
Ref |
Expression |
1 |
|
ovolval5lem1.a |
|
2 |
|
ovolval5lem1.b |
|
3 |
|
ovolval5lem1.w |
|
4 |
|
ovolval5lem1.c |
|
5 |
|
nfv |
|
6 |
|
nnex |
|
7 |
6
|
a1i |
|
8 |
|
volf |
|
9 |
8
|
a1i |
|
10 |
|
ioombl |
|
11 |
10
|
a1i |
|
12 |
9 11
|
ffvelrnd |
|
13 |
5 7 12
|
sge0xrclmpt |
|
14 |
|
0xr |
|
15 |
14
|
a1i |
|
16 |
|
pnfxr |
|
17 |
16
|
a1i |
|
18 |
|
volicore |
|
19 |
1 2 18
|
syl2anc |
|
20 |
3
|
rpred |
|
21 |
20
|
adantr |
|
22 |
|
2nn |
|
23 |
22
|
a1i |
|
24 |
|
nnnn0 |
|
25 |
|
nnexpcl |
|
26 |
23 24 25
|
syl2anc |
|
27 |
26
|
nnred |
|
28 |
27
|
adantl |
|
29 |
26
|
nnne0d |
|
30 |
29
|
adantl |
|
31 |
21 28 30
|
redivcld |
|
32 |
19 31
|
readdcld |
|
33 |
32
|
rexrd |
|
34 |
2
|
rexrd |
|
35 |
|
icombl |
|
36 |
1 34 35
|
syl2anc |
|
37 |
|
volge0 |
|
38 |
36 37
|
syl |
|
39 |
3
|
adantr |
|
40 |
26
|
nnrpd |
|
41 |
40
|
adantl |
|
42 |
39 41
|
rpdivcld |
|
43 |
42
|
rpge0d |
|
44 |
19 31 38 43
|
addge0d |
|
45 |
|
rexr |
|
46 |
16
|
a1i |
|
47 |
|
ltpnf |
|
48 |
45 46 47
|
xrltled |
|
49 |
32 48
|
syl |
|
50 |
15 17 33 44 49
|
eliccxrd |
|
51 |
5 7 50
|
sge0xrclmpt |
|
52 |
9 36
|
ffvelrnd |
|
53 |
5 7 52
|
sge0xrclmpt |
|
54 |
20
|
rexrd |
|
55 |
53 54
|
xaddcld |
|
56 |
1 31
|
resubcld |
|
57 |
|
volioore |
|
58 |
56 2 57
|
syl2anc |
|
59 |
58
|
adantr |
|
60 |
|
iftrue |
|
61 |
60
|
adantl |
|
62 |
2
|
recnd |
|
63 |
1
|
recnd |
|
64 |
31
|
recnd |
|
65 |
62 63 64
|
subsubd |
|
66 |
65
|
adantr |
|
67 |
59 61 66
|
3eqtrd |
|
68 |
2 1
|
resubcld |
|
69 |
1 2
|
sublevolico |
|
70 |
68 19 31 69
|
leadd1dd |
|
71 |
70
|
adantr |
|
72 |
67 71
|
eqbrtrd |
|
73 |
58
|
adantr |
|
74 |
|
iffalse |
|
75 |
74
|
adantl |
|
76 |
73 75
|
eqtrd |
|
77 |
44
|
adantr |
|
78 |
76 77
|
eqbrtrd |
|
79 |
72 78
|
pm2.61dan |
|
80 |
5 7 12 50 79
|
sge0lempt |
|
81 |
19 31
|
rexaddd |
|
82 |
81
|
eqcomd |
|
83 |
82
|
mpteq2dva |
|
84 |
83
|
fveq2d |
|
85 |
31
|
rexrd |
|
86 |
|
rexr |
|
87 |
16
|
a1i |
|
88 |
|
ltpnf |
|
89 |
86 87 88
|
xrltled |
|
90 |
31 89
|
syl |
|
91 |
15 17 85 43 90
|
eliccxrd |
|
92 |
5 7 52 91
|
sge0xadd |
|
93 |
14
|
a1i |
|
94 |
16
|
a1i |
|
95 |
3
|
rpge0d |
|
96 |
20
|
ltpnfd |
|
97 |
93 94 54 95 96
|
elicod |
|
98 |
97
|
sge0ad2en |
|
99 |
98
|
oveq2d |
|
100 |
84 92 99
|
3eqtrd |
|
101 |
51 100
|
xreqled |
|
102 |
13 51 55 80 101
|
xrletrd |
|