Step |
Hyp |
Ref |
Expression |
1 |
|
heibor.1 |
|
2 |
|
heibor.3 |
|
3 |
|
heibor.4 |
|
4 |
|
heibor.5 |
|
5 |
|
heibor.6 |
|
6 |
|
heibor.7 |
|
7 |
|
heibor.8 |
|
8 |
|
heibor.9 |
|
9 |
|
heibor.10 |
|
10 |
|
heibor.11 |
|
11 |
|
heibor.12 |
|
12 |
|
heibor.13 |
|
13 |
|
heibor.14 |
|
14 |
|
heibor.15 |
|
15 |
|
heibor.16 |
|
16 |
|
heibor.17 |
|
17 |
|
cmetmet |
|
18 |
|
metxmet |
|
19 |
5 17 18
|
3syl |
|
20 |
12 15
|
sseldd |
|
21 |
1
|
mopni2 |
|
22 |
19 20 14 21
|
syl3anc |
|
23 |
|
rphalfcl |
|
24 |
|
breq2 |
|
25 |
24
|
rexbidv |
|
26 |
1 2 3 4 5 6 7 8 9 10 11
|
heiborlem7 |
|
27 |
25 26
|
vtoclri |
|
28 |
23 27
|
syl |
|
29 |
28
|
adantl |
|
30 |
|
nnnn0 |
|
31 |
1 2 3 4 5 6 7 8 9 10
|
heiborlem4 |
|
32 |
|
fvex |
|
33 |
|
vex |
|
34 |
1 2 3 32 33
|
heiborlem2 |
|
35 |
34
|
simp3bi |
|
36 |
31 35
|
syl |
|
37 |
30 36
|
sylan2 |
|
38 |
37
|
ad2ant2r |
|
39 |
19
|
ad2antrr |
|
40 |
1 2 3 4 5 6 7 8 9 10 11
|
heiborlem5 |
|
41 |
40
|
ffvelrnda |
|
42 |
41
|
ad2ant2r |
|
43 |
|
xp1st |
|
44 |
42 43
|
syl |
|
45 |
|
2nn |
|
46 |
|
nnexpcl |
|
47 |
45 30 46
|
sylancr |
|
48 |
47
|
nnrpd |
|
49 |
48
|
rpreccld |
|
50 |
49
|
ad2antrl |
|
51 |
50
|
rpxrd |
|
52 |
|
xp2nd |
|
53 |
42 52
|
syl |
|
54 |
53
|
rpxrd |
|
55 |
|
1le3 |
|
56 |
|
elrp |
|
57 |
|
1re |
|
58 |
|
3re |
|
59 |
|
lediv1 |
|
60 |
57 58 59
|
mp3an12 |
|
61 |
56 60
|
sylbi |
|
62 |
55 61
|
mpbii |
|
63 |
48 62
|
syl |
|
64 |
63
|
ad2antrl |
|
65 |
|
fveq2 |
|
66 |
|
oveq2 |
|
67 |
66
|
oveq2d |
|
68 |
65 67
|
opeq12d |
|
69 |
|
opex |
|
70 |
68 11 69
|
fvmpt |
|
71 |
70
|
fveq2d |
|
72 |
|
ovex |
|
73 |
32 72
|
op2nd |
|
74 |
71 73
|
eqtrdi |
|
75 |
74
|
ad2antrl |
|
76 |
64 75
|
breqtrrd |
|
77 |
|
ssbl |
|
78 |
39 44 51 54 76 77
|
syl221anc |
|
79 |
30
|
ad2antrl |
|
80 |
|
oveq1 |
|
81 |
|
oveq2 |
|
82 |
81
|
oveq2d |
|
83 |
82
|
oveq2d |
|
84 |
|
ovex |
|
85 |
80 83 4 84
|
ovmpo |
|
86 |
44 79 85
|
syl2anc |
|
87 |
70
|
fveq2d |
|
88 |
32 72
|
op1st |
|
89 |
87 88
|
eqtrdi |
|
90 |
89
|
ad2antrl |
|
91 |
90
|
oveq1d |
|
92 |
86 91
|
eqtr3d |
|
93 |
|
df-ov |
|
94 |
|
1st2nd2 |
|
95 |
42 94
|
syl |
|
96 |
95
|
fveq2d |
|
97 |
93 96
|
eqtr4id |
|
98 |
78 92 97
|
3sstr3d |
|
99 |
1
|
mopntop |
|
100 |
39 99
|
syl |
|
101 |
|
blssm |
|
102 |
39 44 54 101
|
syl3anc |
|
103 |
1
|
mopnuni |
|
104 |
39 103
|
syl |
|
105 |
102 97 104
|
3sstr3d |
|
106 |
|
eqid |
|
107 |
106
|
sscls |
|
108 |
100 105 107
|
syl2anc |
|
109 |
97
|
fveq2d |
|
110 |
23
|
ad2antlr |
|
111 |
110
|
rpxrd |
|
112 |
|
simprr |
|
113 |
1
|
blsscls |
|
114 |
39 44 54 111 112 113
|
syl23anc |
|
115 |
109 114
|
eqsstrrd |
|
116 |
|
rpre |
|
117 |
116
|
ad2antlr |
|
118 |
1 2 3 4 5 6 7 8 9 10 11
|
heiborlem6 |
|
119 |
19 40 118 1
|
caublcls |
|
120 |
119
|
3expia |
|
121 |
16 120
|
mpdan |
|
122 |
121
|
imp |
|
123 |
122
|
ad2ant2r |
|
124 |
115 123
|
sseldd |
|
125 |
|
blhalf |
|
126 |
39 44 117 124 125
|
syl22anc |
|
127 |
115 126
|
sstrd |
|
128 |
108 127
|
sstrd |
|
129 |
98 128
|
sstrd |
|
130 |
|
sstr2 |
|
131 |
129 130
|
syl |
|
132 |
|
unisng |
|
133 |
15 132
|
syl |
|
134 |
133
|
sseq2d |
|
135 |
134
|
biimpar |
|
136 |
15
|
snssd |
|
137 |
|
snex |
|
138 |
137
|
elpw |
|
139 |
136 138
|
sylibr |
|
140 |
|
snfi |
|
141 |
140
|
a1i |
|
142 |
139 141
|
elind |
|
143 |
|
unieq |
|
144 |
143
|
sseq2d |
|
145 |
144
|
rspcev |
|
146 |
142 145
|
sylan |
|
147 |
135 146
|
syldan |
|
148 |
|
ovex |
|
149 |
|
sseq1 |
|
150 |
149
|
rexbidv |
|
151 |
150
|
notbid |
|
152 |
148 151 2
|
elab2 |
|
153 |
152
|
con2bii |
|
154 |
147 153
|
sylib |
|
155 |
154
|
ex |
|
156 |
155
|
ad2antrr |
|
157 |
131 156
|
syld |
|
158 |
38 157
|
mt2d |
|
159 |
29 158
|
rexlimddv |
|
160 |
159
|
nrexdv |
|
161 |
22 160
|
pm2.21dd |
|