Step |
Hyp |
Ref |
Expression |
1 |
|
ovnhoi.x |
|
2 |
|
ovnhoi.a |
|
3 |
|
ovnhoi.b |
|
4 |
|
ovnhoi.c |
|
5 |
|
ovnhoi.l |
|
6 |
4
|
a1i |
|
7 |
|
nfv |
|
8 |
2
|
ffvelrnda |
|
9 |
3
|
ffvelrnda |
|
10 |
9
|
rexrd |
|
11 |
7 8 10
|
hoissrrn2 |
|
12 |
6 11
|
eqsstrd |
|
13 |
1 12
|
ovnxrcl |
|
14 |
|
icossxr |
|
15 |
5 1 2 3
|
hoidmvcl |
|
16 |
14 15
|
sseldi |
|
17 |
|
fveq2 |
|
18 |
17
|
fveq1d |
|
19 |
18
|
adantl |
|
20 |
|
ixpeq1 |
|
21 |
|
ixp0x |
|
22 |
21
|
a1i |
|
23 |
20 22
|
eqtrd |
|
24 |
23
|
adantl |
|
25 |
4
|
a1i |
|
26 |
|
reex |
|
27 |
|
mapdm0 |
|
28 |
26 27
|
ax-mp |
|
29 |
28
|
a1i |
|
30 |
24 25 29
|
3eqtr4d |
|
31 |
|
eqimss |
|
32 |
30 31
|
syl |
|
33 |
32
|
ovn0val |
|
34 |
19 33
|
eqtrd |
|
35 |
|
0red |
|
36 |
34 35
|
eqeltrd |
|
37 |
|
eqidd |
|
38 |
|
fveq2 |
|
39 |
38
|
oveqd |
|
40 |
39
|
adantl |
|
41 |
2
|
adantr |
|
42 |
|
simpr |
|
43 |
42
|
feq2d |
|
44 |
41 43
|
mpbid |
|
45 |
3
|
adantr |
|
46 |
42
|
feq2d |
|
47 |
45 46
|
mpbid |
|
48 |
5 44 47
|
hoidmv0val |
|
49 |
40 48
|
eqtrd |
|
50 |
37 34 49
|
3eqtr4d |
|
51 |
36 50
|
eqled |
|
52 |
|
eqid |
|
53 |
|
eqeq1 |
|
54 |
53
|
ifbid |
|
55 |
54
|
mpteq2dv |
|
56 |
55
|
cbvmptv |
|
57 |
1 2 3 4 52 56
|
ovnhoilem1 |
|
58 |
57
|
adantr |
|
59 |
1
|
adantr |
|
60 |
|
neqne |
|
61 |
60
|
adantl |
|
62 |
2
|
adantr |
|
63 |
3
|
adantr |
|
64 |
5 59 61 62 63
|
hoidmvn0val |
|
65 |
64
|
eqcomd |
|
66 |
58 65
|
breqtrd |
|
67 |
51 66
|
pm2.61dan |
|
68 |
49 35
|
eqeltrd |
|
69 |
50
|
eqcomd |
|
70 |
68 69
|
eqled |
|
71 |
|
fveq1 |
|
72 |
71
|
fvoveq1d |
|
73 |
72
|
prodeq2ad |
|
74 |
73
|
ifeq2d |
|
75 |
|
fveq1 |
|
76 |
75
|
oveq2d |
|
77 |
76
|
fveq2d |
|
78 |
77
|
prodeq2ad |
|
79 |
78
|
ifeq2d |
|
80 |
74 79
|
cbvmpov |
|
81 |
80
|
a1i |
|
82 |
|
oveq2 |
|
83 |
|
eqeq1 |
|
84 |
|
prodeq1 |
|
85 |
83 84
|
ifbieq2d |
|
86 |
82 82 85
|
mpoeq123dv |
|
87 |
81 86
|
eqtrd |
|
88 |
87
|
cbvmptv |
|
89 |
5 88
|
eqtri |
|
90 |
|
eqeq1 |
|
91 |
90
|
anbi2d |
|
92 |
91
|
rexbidv |
|
93 |
|
simpl |
|
94 |
93
|
fveq1d |
|
95 |
94
|
coeq2d |
|
96 |
95
|
fveq1d |
|
97 |
96
|
ixpeq2dv |
|
98 |
97
|
iuneq2dv |
|
99 |
98
|
sseq2d |
|
100 |
|
simpl |
|
101 |
100
|
fveq1d |
|
102 |
101
|
coeq2d |
|
103 |
102
|
fveq1d |
|
104 |
103
|
fveq2d |
|
105 |
104
|
prodeq2dv |
|
106 |
105
|
mpteq2dv |
|
107 |
106
|
fveq2d |
|
108 |
107
|
eqeq2d |
|
109 |
99 108
|
anbi12d |
|
110 |
109
|
cbvrexvw |
|
111 |
110
|
a1i |
|
112 |
92 111
|
bitrd |
|
113 |
112
|
cbvrabv |
|
114 |
|
simpl |
|
115 |
114
|
fveq2d |
|
116 |
115
|
fveq1d |
|
117 |
116
|
fveq2d |
|
118 |
117
|
mpteq2dva |
|
119 |
118
|
cbvmptv |
|
120 |
119
|
mpteq2i |
|
121 |
116
|
fveq2d |
|
122 |
121
|
mpteq2dva |
|
123 |
122
|
cbvmptv |
|
124 |
123
|
mpteq2i |
|
125 |
59 61 62 63 4 89 113 120 124
|
ovnhoilem2 |
|
126 |
70 125
|
pm2.61dan |
|
127 |
13 16 67 126
|
xrletrid |
|