Step |
Hyp |
Ref |
Expression |
1 |
|
metust.1 |
|
2 |
|
simp-4r |
|
3 |
|
simplr |
|
4 |
3
|
rphalfcld |
|
5 |
|
eqidd |
|
6 |
|
oveq2 |
|
7 |
6
|
imaeq2d |
|
8 |
7
|
rspceeqv |
|
9 |
4 5 8
|
syl2anc |
|
10 |
|
oveq2 |
|
11 |
10
|
imaeq2d |
|
12 |
11
|
cbvmptv |
|
13 |
12
|
rneqi |
|
14 |
1 13
|
eqtri |
|
15 |
14
|
metustel |
|
16 |
15
|
biimpar |
|
17 |
2 9 16
|
syl2anc |
|
18 |
|
relco |
|
19 |
18
|
a1i |
|
20 |
|
cossxp |
|
21 |
|
cnvimass |
|
22 |
|
psmetf |
|
23 |
21 22
|
fssdm |
|
24 |
|
dmss |
|
25 |
|
rnss |
|
26 |
|
xpss12 |
|
27 |
24 25 26
|
syl2anc |
|
28 |
23 27
|
syl |
|
29 |
28
|
adantl |
|
30 |
|
dmxp |
|
31 |
|
rnxp |
|
32 |
30 31
|
xpeq12d |
|
33 |
32
|
adantr |
|
34 |
29 33
|
sseqtrd |
|
35 |
20 34
|
sstrid |
|
36 |
35
|
ad3antrrr |
|
37 |
36
|
sselda |
|
38 |
|
opelxp |
|
39 |
37 38
|
sylib |
|
40 |
|
simpll |
|
41 |
|
simprl |
|
42 |
|
simprr |
|
43 |
|
simplr |
|
44 |
|
simplll |
|
45 |
44
|
simp1d |
|
46 |
45 2
|
syl |
|
47 |
45 3
|
syl |
|
48 |
46 47
|
jca |
|
49 |
44
|
simp2d |
|
50 |
44
|
simp3d |
|
51 |
48 49 50
|
3jca |
|
52 |
|
simplr |
|
53 |
|
simprl |
|
54 |
|
simprr |
|
55 |
|
simpll |
|
56 |
55
|
simp1d |
|
57 |
56
|
simpld |
|
58 |
22
|
ffund |
|
59 |
57 58
|
syl |
|
60 |
55
|
simp2d |
|
61 |
55
|
simp3d |
|
62 |
60 61
|
opelxpd |
|
63 |
22
|
fdmd |
|
64 |
57 63
|
syl |
|
65 |
62 64
|
eleqtrrd |
|
66 |
|
0xr |
|
67 |
66
|
a1i |
|
68 |
56
|
simprd |
|
69 |
68
|
rpxrd |
|
70 |
57 22
|
syl |
|
71 |
70 62
|
ffvelrnd |
|
72 |
|
psmetge0 |
|
73 |
57 60 61 72
|
syl3anc |
|
74 |
|
df-ov |
|
75 |
73 74
|
breqtrdi |
|
76 |
74 71
|
eqeltrid |
|
77 |
|
0red |
|
78 |
68
|
rpred |
|
79 |
78
|
rehalfcld |
|
80 |
79
|
rexrd |
|
81 |
|
df-ov |
|
82 |
|
simplr |
|
83 |
60 82
|
opelxpd |
|
84 |
83 64
|
eleqtrrd |
|
85 |
|
simprl |
|
86 |
|
df-br |
|
87 |
85 86
|
sylib |
|
88 |
|
fvimacnv |
|
89 |
88
|
biimpar |
|
90 |
59 84 87 89
|
syl21anc |
|
91 |
81 90
|
eqeltrid |
|
92 |
|
elico2 |
|
93 |
92
|
biimpa |
|
94 |
93
|
simp1d |
|
95 |
77 80 91 94
|
syl21anc |
|
96 |
|
df-ov |
|
97 |
82 61
|
opelxpd |
|
98 |
97 64
|
eleqtrrd |
|
99 |
|
simprr |
|
100 |
|
df-br |
|
101 |
99 100
|
sylib |
|
102 |
|
fvimacnv |
|
103 |
102
|
biimpar |
|
104 |
59 98 101 103
|
syl21anc |
|
105 |
96 104
|
eqeltrid |
|
106 |
|
elico2 |
|
107 |
106
|
biimpa |
|
108 |
107
|
simp1d |
|
109 |
77 80 105 108
|
syl21anc |
|
110 |
95 109
|
rexaddd |
|
111 |
95 109
|
readdcld |
|
112 |
110 111
|
eqeltrd |
|
113 |
112
|
rexrd |
|
114 |
|
psmettri |
|
115 |
57 60 61 82 114
|
syl13anc |
|
116 |
93
|
simp3d |
|
117 |
77 80 91 116
|
syl21anc |
|
118 |
107
|
simp3d |
|
119 |
77 80 105 118
|
syl21anc |
|
120 |
95 109 78 117 119
|
lt2halvesd |
|
121 |
110 120
|
eqbrtrd |
|
122 |
76 113 69 115 121
|
xrlelttrd |
|
123 |
74 122
|
eqbrtrrid |
|
124 |
67 69 71 75 123
|
elicod |
|
125 |
|
fvimacnv |
|
126 |
125
|
biimpa |
|
127 |
|
df-br |
|
128 |
126 127
|
sylibr |
|
129 |
59 65 124 128
|
syl21anc |
|
130 |
51 52 53 54 129
|
syl22anc |
|
131 |
45
|
simprd |
|
132 |
131
|
breqd |
|
133 |
130 132
|
mpbird |
|
134 |
|
simpr |
|
135 |
|
df-br |
|
136 |
134 135
|
sylibr |
|
137 |
|
vex |
|
138 |
|
vex |
|
139 |
137 138
|
brco |
|
140 |
136 139
|
sylib |
|
141 |
23
|
adantl |
|
142 |
141 25
|
syl |
|
143 |
31
|
adantr |
|
144 |
142 143
|
sseqtrd |
|
145 |
144
|
adantr |
|
146 |
|
vex |
|
147 |
137 146
|
brelrn |
|
148 |
147
|
adantl |
|
149 |
145 148
|
sseldd |
|
150 |
149
|
adantrr |
|
151 |
150
|
ex |
|
152 |
151
|
ancrd |
|
153 |
152
|
eximdv |
|
154 |
153
|
ad3antrrr |
|
155 |
154
|
3ad2ant1 |
|
156 |
155
|
adantr |
|
157 |
140 156
|
mpd |
|
158 |
|
df-rex |
|
159 |
157 158
|
sylibr |
|
160 |
133 159
|
r19.29a |
|
161 |
|
df-br |
|
162 |
160 161
|
sylib |
|
163 |
40 41 42 43 162
|
syl31anc |
|
164 |
39 163
|
mpdan |
|
165 |
164
|
ex |
|
166 |
19 165
|
relssdv |
|
167 |
|
id |
|
168 |
167 167
|
coeq12d |
|
169 |
168
|
sseq1d |
|
170 |
169
|
rspcev |
|
171 |
17 166 170
|
syl2anc |
|
172 |
1
|
metustel |
|
173 |
172
|
adantl |
|
174 |
173
|
biimpa |
|
175 |
171 174
|
r19.29a |
|