Step |
Hyp |
Ref |
Expression |
1 |
|
ovn0lem.x |
|
2 |
|
ovn0lem.n0 |
|
3 |
|
ovn0lem.m |
|
4 |
|
ovn0lem.infm |
|
5 |
|
ovn0lem.i |
|
6 |
|
iccssxr |
|
7 |
6 4
|
sseldi |
|
8 |
|
0xr |
|
9 |
8
|
a1i |
|
10 |
|
ssrab2 |
|
11 |
3 10
|
eqsstri |
|
12 |
11
|
a1i |
|
13 |
|
1re |
|
14 |
|
0re |
|
15 |
13 14
|
pm3.2i |
|
16 |
|
opelxp |
|
17 |
15 16
|
mpbir |
|
18 |
17
|
a1i |
|
19 |
|
eqid |
|
20 |
18 19
|
fmptd |
|
21 |
|
reex |
|
22 |
21 21
|
xpex |
|
23 |
22
|
a1i |
|
24 |
|
elmapg |
|
25 |
23 1 24
|
syl2anc |
|
26 |
20 25
|
mpbird |
|
27 |
26
|
adantr |
|
28 |
27 5
|
fmptd |
|
29 |
|
ovexd |
|
30 |
|
nnex |
|
31 |
30
|
a1i |
|
32 |
|
elmapg |
|
33 |
29 31 32
|
syl2anc |
|
34 |
28 33
|
mpbird |
|
35 |
|
n0 |
|
36 |
2 35
|
sylib |
|
37 |
36
|
adantr |
|
38 |
|
nfv |
|
39 |
|
nfcv |
|
40 |
1
|
ad2antrr |
|
41 |
28
|
ffvelrnda |
|
42 |
|
elmapi |
|
43 |
41 42
|
syl |
|
44 |
43
|
adantr |
|
45 |
|
simpr |
|
46 |
44 45
|
fvovco |
|
47 |
|
simpr |
|
48 |
27
|
elexd |
|
49 |
5
|
fvmpt2 |
|
50 |
47 48 49
|
syl2anc |
|
51 |
50
|
adantr |
|
52 |
|
eqidd |
|
53 |
17
|
elexi |
|
54 |
53
|
a1i |
|
55 |
51 52 45 54
|
fvmptd |
|
56 |
55
|
fveq2d |
|
57 |
13
|
elexi |
|
58 |
8
|
elexi |
|
59 |
57 58
|
op1st |
|
60 |
59
|
a1i |
|
61 |
56 60
|
eqtrd |
|
62 |
55
|
fveq2d |
|
63 |
57 58
|
op2nd |
|
64 |
63
|
a1i |
|
65 |
62 64
|
eqtrd |
|
66 |
61 65
|
oveq12d |
|
67 |
|
0le1 |
|
68 |
|
1xr |
|
69 |
|
ico0 |
|
70 |
68 8 69
|
mp2an |
|
71 |
67 70
|
mpbir |
|
72 |
71
|
a1i |
|
73 |
46 66 72
|
3eqtrd |
|
74 |
73
|
fveq2d |
|
75 |
|
vol0 |
|
76 |
75
|
a1i |
|
77 |
74 76
|
eqtrd |
|
78 |
|
0cn |
|
79 |
78
|
a1i |
|
80 |
77 79
|
eqeltrd |
|
81 |
80
|
adantlr |
|
82 |
|
2fveq3 |
|
83 |
|
simpr |
|
84 |
|
eleq1w |
|
85 |
84
|
anbi2d |
|
86 |
82
|
eqeq1d |
|
87 |
85 86
|
imbi12d |
|
88 |
87 77
|
chvarvv |
|
89 |
38 39 40 81 82 83 88
|
fprod0 |
|
90 |
89
|
ex |
|
91 |
90
|
exlimdv |
|
92 |
37 91
|
mpd |
|
93 |
92
|
mpteq2dva |
|
94 |
93
|
fveq2d |
|
95 |
|
nfv |
|
96 |
95 31
|
sge0z |
|
97 |
|
eqidd |
|
98 |
94 96 97
|
3eqtrrd |
|
99 |
|
fveq1 |
|
100 |
99
|
coeq2d |
|
101 |
100
|
fveq1d |
|
102 |
101
|
fveq2d |
|
103 |
102
|
ralrimivw |
|
104 |
103
|
prodeq2d |
|
105 |
104
|
mpteq2dv |
|
106 |
105
|
fveq2d |
|
107 |
106
|
rspceeqv |
|
108 |
34 98 107
|
syl2anc |
|
109 |
9 108
|
jca |
|
110 |
|
eqeq1 |
|
111 |
110
|
rexbidv |
|
112 |
111 3
|
elrab2 |
|
113 |
109 112
|
sylibr |
|
114 |
|
infxrlb |
|
115 |
12 113 114
|
syl2anc |
|
116 |
|
pnfxr |
|
117 |
116
|
a1i |
|
118 |
|
iccgelb |
|
119 |
9 117 4 118
|
syl3anc |
|
120 |
7 9 115 119
|
xrletrid |
|