Step |
Hyp |
Ref |
Expression |
1 |
|
hoicvrrex.fi |
|
2 |
|
hoicvrrex.y |
|
3 |
|
nnre |
|
4 |
3
|
renegcld |
|
5 |
|
opelxpi |
|
6 |
4 3 5
|
syl2anc |
|
7 |
6
|
ad2antlr |
|
8 |
|
eqid |
|
9 |
7 8
|
fmptd |
|
10 |
|
reex |
|
11 |
10 10
|
xpex |
|
12 |
11
|
a1i |
|
13 |
|
elmapg |
|
14 |
12 1 13
|
syl2anc |
|
15 |
14
|
adantr |
|
16 |
9 15
|
mpbird |
|
17 |
|
eqid |
|
18 |
16 17
|
fmptd |
|
19 |
|
ovex |
|
20 |
|
nnex |
|
21 |
19 20
|
elmap |
|
22 |
18 21
|
sylibr |
|
23 |
|
eqid |
|
24 |
23 1
|
hoicvr |
|
25 |
|
eqidd |
|
26 |
25
|
cbvmptv |
|
27 |
26
|
mpteq2i |
|
28 |
27
|
a1i |
|
29 |
28
|
fveq1d |
|
30 |
29
|
coeq2d |
|
31 |
30
|
fveq1d |
|
32 |
31
|
ixpeq2dv |
|
33 |
32
|
iuneq2d |
|
34 |
24 33
|
sseqtrd |
|
35 |
2 34
|
sstrd |
|
36 |
|
simpr |
|
37 |
16
|
elexd |
|
38 |
17
|
fvmpt2 |
|
39 |
36 37 38
|
syl2anc |
|
40 |
39 7
|
fmpt3d |
|
41 |
40
|
adantr |
|
42 |
|
simpr |
|
43 |
41 42
|
fvovco |
|
44 |
39
|
fveq1d |
|
45 |
44
|
adantr |
|
46 |
|
simpr |
|
47 |
|
opex |
|
48 |
47
|
a1i |
|
49 |
8
|
fvmpt2 |
|
50 |
46 48 49
|
syl2anc |
|
51 |
50
|
adantlr |
|
52 |
45 51
|
eqtrd |
|
53 |
52
|
fveq2d |
|
54 |
|
negex |
|
55 |
|
vex |
|
56 |
54 55
|
op1st |
|
57 |
56
|
a1i |
|
58 |
53 57
|
eqtrd |
|
59 |
52
|
fveq2d |
|
60 |
54 55
|
op2nd |
|
61 |
60
|
a1i |
|
62 |
59 61
|
eqtrd |
|
63 |
58 62
|
oveq12d |
|
64 |
43 63
|
eqtrd |
|
65 |
64
|
fveq2d |
|
66 |
|
volico |
|
67 |
4 3 66
|
syl2anc |
|
68 |
|
nnrp |
|
69 |
|
neglt |
|
70 |
68 69
|
syl |
|
71 |
70
|
iftrued |
|
72 |
3
|
recnd |
|
73 |
72 72
|
subnegd |
|
74 |
72
|
2timesd |
|
75 |
73 74
|
eqtr4d |
|
76 |
67 71 75
|
3eqtrd |
|
77 |
76
|
ad2antlr |
|
78 |
65 77
|
eqtrd |
|
79 |
78
|
prodeq2dv |
|
80 |
1
|
adantr |
|
81 |
|
2cnd |
|
82 |
72
|
adantl |
|
83 |
81 82
|
mulcld |
|
84 |
|
fprodconst |
|
85 |
80 83 84
|
syl2anc |
|
86 |
79 85
|
eqtrd |
|
87 |
86
|
mpteq2dva |
|
88 |
87
|
fveq2d |
|
89 |
20
|
a1i |
|
90 |
68
|
ssriv |
|
91 |
|
ioorp |
|
92 |
91
|
eqcomi |
|
93 |
90 92
|
sseqtri |
|
94 |
|
ioossicc |
|
95 |
93 94
|
sstri |
|
96 |
|
2nn |
|
97 |
96
|
a1i |
|
98 |
97 36
|
nnmulcld |
|
99 |
|
hashcl |
|
100 |
1 99
|
syl |
|
101 |
100
|
adantr |
|
102 |
|
nnexpcl |
|
103 |
98 101 102
|
syl2anc |
|
104 |
95 103
|
sselid |
|
105 |
|
eqid |
|
106 |
104 105
|
fmptd |
|
107 |
89 106
|
sge0xrcl |
|
108 |
|
pnfxr |
|
109 |
108
|
a1i |
|
110 |
|
1nn |
|
111 |
95 110
|
sselii |
|
112 |
111
|
a1i |
|
113 |
|
eqid |
|
114 |
112 113
|
fmptd |
|
115 |
89 114
|
sge0xrcl |
|
116 |
|
nnnfi |
|
117 |
116
|
a1i |
|
118 |
|
1rp |
|
119 |
118
|
a1i |
|
120 |
89 117 119
|
sge0rpcpnf |
|
121 |
120
|
eqcomd |
|
122 |
109 121
|
xreqled |
|
123 |
|
nfv |
|
124 |
114
|
fvmptelrn |
|
125 |
103
|
nnge1d |
|
126 |
123 89 124 104 125
|
sge0lempt |
|
127 |
109 115 107 122 126
|
xrletrd |
|
128 |
107 127
|
xrgepnfd |
|
129 |
|
eqidd |
|
130 |
88 128 129
|
3eqtrrd |
|
131 |
35 130
|
jca |
|
132 |
|
nfcv |
|
133 |
|
nfmpt1 |
|
134 |
132 133
|
nfeq |
|
135 |
|
nfcv |
|
136 |
|
nfcv |
|
137 |
|
nfmpt1 |
|
138 |
136 137
|
nfmpt |
|
139 |
135 138
|
nfeq |
|
140 |
|
fveq1 |
|
141 |
140
|
coeq2d |
|
142 |
141
|
fveq1d |
|
143 |
142
|
adantr |
|
144 |
139 143
|
ixpeq2d |
|
145 |
144
|
adantr |
|
146 |
134 145
|
iuneq2df |
|
147 |
146
|
sseq2d |
|
148 |
142
|
fveq2d |
|
149 |
148
|
a1d |
|
150 |
139 149
|
ralrimi |
|
151 |
150
|
adantr |
|
152 |
151
|
prodeq2d |
|
153 |
134 152
|
mpteq2da |
|
154 |
153
|
fveq2d |
|
155 |
154
|
eqeq2d |
|
156 |
147 155
|
anbi12d |
|
157 |
156
|
rspcev |
|
158 |
22 131 157
|
syl2anc |
|