Step |
Hyp |
Ref |
Expression |
1 |
|
prdsdsf.y |
|
2 |
|
prdsdsf.b |
|
3 |
|
prdsdsf.v |
|
4 |
|
prdsdsf.e |
|
5 |
|
prdsdsf.d |
|
6 |
|
prdsdsf.s |
|
7 |
|
prdsdsf.i |
|
8 |
|
prdsdsf.r |
|
9 |
|
prdsdsf.m |
|
10 |
2
|
fvexi |
|
11 |
10
|
a1i |
|
12 |
1 2 3 4 5 6 7 8 9
|
prdsdsf |
|
13 |
|
iccssxr |
|
14 |
|
fss |
|
15 |
12 13 14
|
sylancl |
|
16 |
12
|
fovrnda |
|
17 |
|
elxrge0 |
|
18 |
17
|
simprbi |
|
19 |
16 18
|
syl |
|
20 |
6
|
adantr |
|
21 |
7
|
adantr |
|
22 |
8
|
ralrimiva |
|
23 |
22
|
adantr |
|
24 |
|
simprl |
|
25 |
|
simprr |
|
26 |
1 2 20 21 23 24 25 3 4 5
|
prdsdsval3 |
|
27 |
26
|
breq1d |
|
28 |
9
|
adantlr |
|
29 |
1 2 20 21 23 3 24
|
prdsbascl |
|
30 |
29
|
r19.21bi |
|
31 |
1 2 20 21 23 3 25
|
prdsbascl |
|
32 |
31
|
r19.21bi |
|
33 |
|
xmetcl |
|
34 |
28 30 32 33
|
syl3anc |
|
35 |
34
|
fmpttd |
|
36 |
35
|
frnd |
|
37 |
|
0xr |
|
38 |
37
|
a1i |
|
39 |
38
|
snssd |
|
40 |
36 39
|
unssd |
|
41 |
|
supxrleub |
|
42 |
40 37 41
|
sylancl |
|
43 |
|
0le0 |
|
44 |
|
c0ex |
|
45 |
|
breq1 |
|
46 |
44 45
|
ralsn |
|
47 |
43 46
|
mpbir |
|
48 |
|
ralunb |
|
49 |
47 48
|
mpbiran2 |
|
50 |
|
ovex |
|
51 |
50
|
rgenw |
|
52 |
|
eqid |
|
53 |
|
breq1 |
|
54 |
52 53
|
ralrnmptw |
|
55 |
51 54
|
ax-mp |
|
56 |
49 55
|
bitri |
|
57 |
|
xmetge0 |
|
58 |
28 30 32 57
|
syl3anc |
|
59 |
58
|
biantrud |
|
60 |
|
xrletri3 |
|
61 |
34 37 60
|
sylancl |
|
62 |
|
xmeteq0 |
|
63 |
28 30 32 62
|
syl3anc |
|
64 |
59 61 63
|
3bitr2d |
|
65 |
64
|
ralbidva |
|
66 |
|
eqid |
|
67 |
66
|
fnmpt |
|
68 |
22 67
|
syl |
|
69 |
68
|
adantr |
|
70 |
1 2 20 21 69 24
|
prdsbasfn |
|
71 |
1 2 20 21 69 25
|
prdsbasfn |
|
72 |
|
eqfnfv |
|
73 |
70 71 72
|
syl2anc |
|
74 |
65 73
|
bitr4d |
|
75 |
56 74
|
syl5bb |
|
76 |
27 42 75
|
3bitrd |
|
77 |
26
|
3adantr3 |
|
78 |
77
|
3adant3 |
|
79 |
9
|
3ad2antl1 |
|
80 |
29
|
3adantr3 |
|
81 |
80
|
3adant3 |
|
82 |
81
|
r19.21bi |
|
83 |
31
|
3adantr3 |
|
84 |
83
|
3adant3 |
|
85 |
84
|
r19.21bi |
|
86 |
79 82 85 33
|
syl3anc |
|
87 |
6
|
3ad2ant1 |
|
88 |
7
|
3ad2ant1 |
|
89 |
22
|
3ad2ant1 |
|
90 |
|
simp23 |
|
91 |
1 2 87 88 89 3 90
|
prdsbascl |
|
92 |
91
|
r19.21bi |
|
93 |
|
xmetcl |
|
94 |
79 92 82 93
|
syl3anc |
|
95 |
|
simp3l |
|
96 |
95
|
adantr |
|
97 |
|
xmetge0 |
|
98 |
79 92 82 97
|
syl3anc |
|
99 |
94
|
fmpttd |
|
100 |
99
|
frnd |
|
101 |
37
|
a1i |
|
102 |
101
|
snssd |
|
103 |
100 102
|
unssd |
|
104 |
|
ssun1 |
|
105 |
|
ovex |
|
106 |
105
|
elabrex |
|
107 |
106
|
adantl |
|
108 |
|
eqid |
|
109 |
108
|
rnmpt |
|
110 |
107 109
|
eleqtrrdi |
|
111 |
104 110
|
sseldi |
|
112 |
|
supxrub |
|
113 |
103 111 112
|
syl2an2r |
|
114 |
|
simp21 |
|
115 |
1 2 87 88 89 90 114 3 4 5
|
prdsdsval3 |
|
116 |
115
|
adantr |
|
117 |
113 116
|
breqtrrd |
|
118 |
|
xrrege0 |
|
119 |
94 96 98 117 118
|
syl22anc |
|
120 |
|
xmetcl |
|
121 |
79 92 85 120
|
syl3anc |
|
122 |
|
simp3r |
|
123 |
122
|
adantr |
|
124 |
|
xmetge0 |
|
125 |
79 92 85 124
|
syl3anc |
|
126 |
121
|
fmpttd |
|
127 |
126
|
frnd |
|
128 |
127 102
|
unssd |
|
129 |
|
ssun1 |
|
130 |
|
ovex |
|
131 |
130
|
elabrex |
|
132 |
131
|
adantl |
|
133 |
|
eqid |
|
134 |
133
|
rnmpt |
|
135 |
132 134
|
eleqtrrdi |
|
136 |
129 135
|
sseldi |
|
137 |
|
supxrub |
|
138 |
128 136 137
|
syl2an2r |
|
139 |
|
simp22 |
|
140 |
1 2 87 88 89 90 139 3 4 5
|
prdsdsval3 |
|
141 |
140
|
adantr |
|
142 |
138 141
|
breqtrrd |
|
143 |
|
xrrege0 |
|
144 |
121 123 125 142 143
|
syl22anc |
|
145 |
119 144
|
readdcld |
|
146 |
79 82 85 57
|
syl3anc |
|
147 |
|
xmettri2 |
|
148 |
79 92 82 85 147
|
syl13anc |
|
149 |
119 144
|
rexaddd |
|
150 |
148 149
|
breqtrd |
|
151 |
|
xrrege0 |
|
152 |
86 145 146 150 151
|
syl22anc |
|
153 |
|
readdcl |
|
154 |
153
|
3ad2ant3 |
|
155 |
154
|
adantr |
|
156 |
119 144 96 123 117 142
|
le2addd |
|
157 |
152 145 155 150 156
|
letrd |
|
158 |
157
|
ralrimiva |
|
159 |
86
|
ralrimiva |
|
160 |
|
breq1 |
|
161 |
52 160
|
ralrnmptw |
|
162 |
159 161
|
syl |
|
163 |
158 162
|
mpbird |
|
164 |
12
|
3ad2ant1 |
|
165 |
164 90 114
|
fovrnd |
|
166 |
|
elxrge0 |
|
167 |
166
|
simprbi |
|
168 |
165 167
|
syl |
|
169 |
164 90 139
|
fovrnd |
|
170 |
|
elxrge0 |
|
171 |
170
|
simprbi |
|
172 |
169 171
|
syl |
|
173 |
95 122 168 172
|
addge0d |
|
174 |
|
breq1 |
|
175 |
44 174
|
ralsn |
|
176 |
173 175
|
sylibr |
|
177 |
|
ralunb |
|
178 |
163 176 177
|
sylanbrc |
|
179 |
40
|
3adantr3 |
|
180 |
179
|
3adant3 |
|
181 |
154
|
rexrd |
|
182 |
|
supxrleub |
|
183 |
180 181 182
|
syl2anc |
|
184 |
178 183
|
mpbird |
|
185 |
78 184
|
eqbrtrd |
|
186 |
11 15 19 76 185
|
isxmet2d |
|