Step |
Hyp |
Ref |
Expression |
1 |
|
ovnhoilem2.x |
|
2 |
|
ovnhoilem2.n |
|
3 |
|
ovnhoilem2.a |
|
4 |
|
ovnhoilem2.b |
|
5 |
|
ovnhoilem2.i |
|
6 |
|
ovnhoilem2.l |
|
7 |
|
ovnhoilem2.m |
|
8 |
|
ovnhoilem2.f |
|
9 |
|
ovnhoilem2.s |
|
10 |
7
|
eleq2i |
|
11 |
|
rabid |
|
12 |
10 11
|
bitri |
|
13 |
12
|
biimpi |
|
14 |
13
|
simprd |
|
15 |
14
|
adantl |
|
16 |
1
|
3ad2ant1 |
|
17 |
3
|
3ad2ant1 |
|
18 |
4
|
3ad2ant1 |
|
19 |
|
elmapi |
|
20 |
19
|
ffvelrnda |
|
21 |
|
elmapi |
|
22 |
20 21
|
syl |
|
23 |
22
|
ffvelrnda |
|
24 |
|
xp1st |
|
25 |
23 24
|
syl |
|
26 |
25
|
fmpttd |
|
27 |
|
reex |
|
28 |
27
|
a1i |
|
29 |
|
1nn |
|
30 |
29
|
a1i |
|
31 |
19 30
|
ffvelrnd |
|
32 |
|
elmapex |
|
33 |
32
|
simprd |
|
34 |
31 33
|
syl |
|
35 |
34
|
adantr |
|
36 |
|
elmapg |
|
37 |
28 35 36
|
syl2anc |
|
38 |
26 37
|
mpbird |
|
39 |
38
|
fmpttd |
|
40 |
|
id |
|
41 |
|
nnex |
|
42 |
41
|
mptex |
|
43 |
42
|
a1i |
|
44 |
8
|
fvmpt2 |
|
45 |
40 43 44
|
syl2anc |
|
46 |
45
|
feq1d |
|
47 |
39 46
|
mpbird |
|
48 |
47
|
3ad2ant2 |
|
49 |
|
xp2nd |
|
50 |
23 49
|
syl |
|
51 |
50
|
fmpttd |
|
52 |
|
elmapg |
|
53 |
28 35 52
|
syl2anc |
|
54 |
51 53
|
mpbird |
|
55 |
54
|
fmpttd |
|
56 |
41
|
mptex |
|
57 |
56
|
a1i |
|
58 |
9
|
fvmpt2 |
|
59 |
40 57 58
|
syl2anc |
|
60 |
59
|
feq1d |
|
61 |
55 60
|
mpbird |
|
62 |
61
|
3ad2ant2 |
|
63 |
|
simp3 |
|
64 |
5
|
a1i |
|
65 |
|
fveq2 |
|
66 |
65
|
fveq1d |
|
67 |
66
|
fveq2d |
|
68 |
66
|
fveq2d |
|
69 |
67 68
|
oveq12d |
|
70 |
69
|
ixpeq2dv |
|
71 |
70
|
cbviunv |
|
72 |
71
|
a1i |
|
73 |
19
|
ffvelrnda |
|
74 |
|
elmapi |
|
75 |
73 74
|
syl |
|
76 |
75
|
adantr |
|
77 |
|
simpr |
|
78 |
76 77
|
fvovco |
|
79 |
78
|
ixpeq2dva |
|
80 |
79
|
iuneq2dv |
|
81 |
|
simpl |
|
82 |
42
|
a1i |
|
83 |
81 82 44
|
syl2anc |
|
84 |
83
|
fveq1d |
|
85 |
|
simpr |
|
86 |
|
mptexg |
|
87 |
34 86
|
syl |
|
88 |
87
|
adantr |
|
89 |
|
eqid |
|
90 |
89
|
fvmpt2 |
|
91 |
85 88 90
|
syl2anc |
|
92 |
84 91
|
eqtrd |
|
93 |
92
|
fveq1d |
|
94 |
93
|
adantr |
|
95 |
|
eqidd |
|
96 |
|
simpr |
|
97 |
96
|
fveq2d |
|
98 |
97
|
fveq2d |
|
99 |
|
simpr |
|
100 |
|
fvexd |
|
101 |
95 98 99 100
|
fvmptd |
|
102 |
101
|
adantlr |
|
103 |
94 102
|
eqtrd |
|
104 |
59
|
fveq1d |
|
105 |
104
|
adantr |
|
106 |
|
mptexg |
|
107 |
34 106
|
syl |
|
108 |
107
|
adantr |
|
109 |
|
eqid |
|
110 |
109
|
fvmpt2 |
|
111 |
85 108 110
|
syl2anc |
|
112 |
105 111
|
eqtrd |
|
113 |
112
|
fveq1d |
|
114 |
113
|
adantr |
|
115 |
|
eqidd |
|
116 |
|
2fveq3 |
|
117 |
116
|
adantl |
|
118 |
|
fvexd |
|
119 |
115 117 99 118
|
fvmptd |
|
120 |
119
|
adantlr |
|
121 |
114 120
|
eqtrd |
|
122 |
103 121
|
oveq12d |
|
123 |
122
|
ixpeq2dva |
|
124 |
123
|
iuneq2dv |
|
125 |
72 80 124
|
3eqtr4d |
|
126 |
125
|
adantl |
|
127 |
126
|
3adant3 |
|
128 |
64 127
|
sseq12d |
|
129 |
63 128
|
mpbid |
|
130 |
129
|
3adant3r |
|
131 |
6 16 17 18 48 62 130
|
hoidmvle |
|
132 |
|
simpl |
|
133 |
132
|
fveq2d |
|
134 |
133
|
fveq1d |
|
135 |
134
|
fveq2d |
|
136 |
135
|
mpteq2dva |
|
137 |
136
|
fveq1d |
|
138 |
137
|
adantr |
|
139 |
|
eqidd |
|
140 |
|
2fveq3 |
|
141 |
140
|
adantl |
|
142 |
|
id |
|
143 |
|
fvexd |
|
144 |
139 141 142 143
|
fvmptd |
|
145 |
144
|
adantl |
|
146 |
138 145
|
eqtrd |
|
147 |
134
|
fveq2d |
|
148 |
147
|
mpteq2dva |
|
149 |
148
|
fveq1d |
|
150 |
149
|
adantr |
|
151 |
|
eqidd |
|
152 |
|
2fveq3 |
|
153 |
152
|
adantl |
|
154 |
|
fvexd |
|
155 |
151 153 142 154
|
fvmptd |
|
156 |
155
|
adantl |
|
157 |
150 156
|
eqtrd |
|
158 |
146 157
|
oveq12d |
|
159 |
158
|
fveq2d |
|
160 |
159
|
prodeq2dv |
|
161 |
160
|
cbvmptv |
|
162 |
161
|
a1i |
|
163 |
78
|
eqcomd |
|
164 |
163
|
fveq2d |
|
165 |
164
|
prodeq2dv |
|
166 |
165
|
mpteq2dva |
|
167 |
162 166
|
eqtrd |
|
168 |
167
|
fveq2d |
|
169 |
168
|
3ad2ant2 |
|
170 |
92
|
adantll |
|
171 |
112
|
adantll |
|
172 |
170 171
|
oveq12d |
|
173 |
1
|
ad2antrr |
|
174 |
2
|
ad2antrr |
|
175 |
23
|
adantlll |
|
176 |
175 24
|
syl |
|
177 |
176
|
fmpttd |
|
178 |
175 49
|
syl |
|
179 |
178
|
fmpttd |
|
180 |
6 173 174 177 179
|
hoidmvn0val |
|
181 |
172 180
|
eqtrd |
|
182 |
181
|
mpteq2dva |
|
183 |
182
|
fveq2d |
|
184 |
183
|
3adant3 |
|
185 |
|
simp3 |
|
186 |
169 184 185
|
3eqtr4d |
|
187 |
186
|
3adant3l |
|
188 |
131 187
|
breqtrd |
|
189 |
188
|
3exp |
|
190 |
189
|
adantr |
|
191 |
190
|
rexlimdv |
|
192 |
15 191
|
mpd |
|
193 |
192
|
ralrimiva |
|
194 |
|
ssrab2 |
|
195 |
7 194
|
eqsstri |
|
196 |
195
|
a1i |
|
197 |
|
icossxr |
|
198 |
6 1 3 4
|
hoidmvcl |
|
199 |
197 198
|
sselid |
|
200 |
|
infxrgelb |
|
201 |
196 199 200
|
syl2anc |
|
202 |
193 201
|
mpbird |
|
203 |
5
|
a1i |
|
204 |
|
nfv |
|
205 |
3
|
ffvelrnda |
|
206 |
4
|
ffvelrnda |
|
207 |
206
|
rexrd |
|
208 |
204 205 207
|
hoissrrn2 |
|
209 |
203 208
|
eqsstrd |
|
210 |
1 2 209 7
|
ovnn0val |
|
211 |
210
|
eqcomd |
|
212 |
202 211
|
breqtrd |
|