Step |
Hyp |
Ref |
Expression |
1 |
|
icccmp.1 |
|
2 |
|
icccmp.2 |
|
3 |
|
icccmp.3 |
|
4 |
|
icccmp.4 |
|
5 |
|
icccmp.5 |
|
6 |
|
icccmp.6 |
|
7 |
|
icccmp.7 |
|
8 |
|
icccmp.8 |
|
9 |
|
icccmp.9 |
|
10 |
|
icccmp.10 |
|
11 |
|
icccmp.11 |
|
12 |
|
icccmp.12 |
|
13 |
|
icccmp.13 |
|
14 |
|
icccmp.14 |
|
15 |
4
|
ssrab3 |
|
16 |
|
iccssre |
|
17 |
5 6 16
|
syl2anc |
|
18 |
15 17
|
sstrid |
|
19 |
1 2 3 4 5 6 7 8 9
|
icccmplem1 |
|
20 |
19
|
simpld |
|
21 |
20
|
ne0d |
|
22 |
19
|
simprd |
|
23 |
|
brralrspcev |
|
24 |
6 22 23
|
syl2anc |
|
25 |
18 21 24
|
suprcld |
|
26 |
13 25
|
eqeltrid |
|
27 |
11
|
rphalfcld |
|
28 |
26 27
|
ltaddrpd |
|
29 |
27
|
rpred |
|
30 |
26 29
|
readdcld |
|
31 |
26 30
|
ltnled |
|
32 |
28 31
|
mpbid |
|
33 |
30 6
|
ifcld |
|
34 |
14 33
|
eqeltrid |
|
35 |
18 21 24 20
|
suprubd |
|
36 |
35 13
|
breqtrrdi |
|
37 |
26 30 28
|
ltled |
|
38 |
5 26 30 36 37
|
letrd |
|
39 |
|
breq2 |
|
40 |
|
breq2 |
|
41 |
39 40
|
ifboth |
|
42 |
38 7 41
|
syl2anc |
|
43 |
42 14
|
breqtrrdi |
|
44 |
|
min2 |
|
45 |
30 6 44
|
syl2anc |
|
46 |
14 45
|
eqbrtrid |
|
47 |
|
elicc2 |
|
48 |
5 6 47
|
syl2anc |
|
49 |
34 43 46 48
|
mpbir3and |
|
50 |
26 11
|
ltsubrpd |
|
51 |
50 13
|
breqtrdi |
|
52 |
11
|
rpred |
|
53 |
26 52
|
resubcld |
|
54 |
|
suprlub |
|
55 |
18 21 24 53 54
|
syl31anc |
|
56 |
51 55
|
mpbid |
|
57 |
|
oveq2 |
|
58 |
57
|
sseq1d |
|
59 |
58
|
rexbidv |
|
60 |
59 4
|
elrab2 |
|
61 |
|
unieq |
|
62 |
61
|
sseq2d |
|
63 |
62
|
cbvrexvw |
|
64 |
|
simpr1 |
|
65 |
|
elin |
|
66 |
64 65
|
sylib |
|
67 |
66
|
simpld |
|
68 |
67
|
elpwid |
|
69 |
|
simpll |
|
70 |
69 10
|
syl |
|
71 |
70
|
snssd |
|
72 |
68 71
|
unssd |
|
73 |
|
vex |
|
74 |
|
snex |
|
75 |
73 74
|
unex |
|
76 |
75
|
elpw |
|
77 |
72 76
|
sylibr |
|
78 |
66
|
simprd |
|
79 |
|
snfi |
|
80 |
|
unfi |
|
81 |
78 79 80
|
sylancl |
|
82 |
77 81
|
elind |
|
83 |
|
simplr2 |
|
84 |
|
ssun1 |
|
85 |
83 84
|
sstrdi |
|
86 |
69 5
|
syl |
|
87 |
69 34
|
syl |
|
88 |
|
elicc2 |
|
89 |
86 87 88
|
syl2anc |
|
90 |
89
|
biimpa |
|
91 |
90
|
simp1d |
|
92 |
91
|
adantrr |
|
93 |
90
|
simp2d |
|
94 |
93
|
adantrr |
|
95 |
|
simprr |
|
96 |
69 17
|
syl |
|
97 |
|
simplr |
|
98 |
96 97
|
sseldd |
|
99 |
|
elicc2 |
|
100 |
86 98 99
|
syl2anc |
|
101 |
100
|
adantr |
|
102 |
92 94 95 101
|
mpbir3and |
|
103 |
85 102
|
sseldd |
|
104 |
103
|
expr |
|
105 |
69
|
adantr |
|
106 |
105 12
|
syl |
|
107 |
91
|
adantrr |
|
108 |
105 53
|
syl |
|
109 |
98
|
adantr |
|
110 |
|
simplr3 |
|
111 |
|
simprr |
|
112 |
108 109 107 110 111
|
lttrd |
|
113 |
105 34
|
syl |
|
114 |
26 52
|
readdcld |
|
115 |
105 114
|
syl |
|
116 |
90
|
simp3d |
|
117 |
116
|
adantrr |
|
118 |
|
min1 |
|
119 |
30 6 118
|
syl2anc |
|
120 |
14 119
|
eqbrtrid |
|
121 |
|
rphalflt |
|
122 |
11 121
|
syl |
|
123 |
29 52 26 122
|
ltadd2dd |
|
124 |
34 30 114 120 123
|
lelttrd |
|
125 |
105 124
|
syl |
|
126 |
107 113 115 117 125
|
lelttrd |
|
127 |
|
rexr |
|
128 |
|
rexr |
|
129 |
|
elioo2 |
|
130 |
127 128 129
|
syl2an |
|
131 |
108 115 130
|
syl2anc |
|
132 |
107 112 126 131
|
mpbir3and |
|
133 |
105 26
|
syl |
|
134 |
105 11
|
syl |
|
135 |
134
|
rpred |
|
136 |
3
|
bl2ioo |
|
137 |
133 135 136
|
syl2anc |
|
138 |
132 137
|
eleqtrrd |
|
139 |
106 138
|
sseldd |
|
140 |
|
elun2 |
|
141 |
139 140
|
syl |
|
142 |
141
|
expr |
|
143 |
98
|
adantr |
|
144 |
|
lelttric |
|
145 |
91 143 144
|
syl2anc |
|
146 |
104 142 145
|
mpjaod |
|
147 |
146
|
ex |
|
148 |
147
|
ssrdv |
|
149 |
|
uniun |
|
150 |
|
unisng |
|
151 |
70 150
|
syl |
|
152 |
151
|
uneq2d |
|
153 |
149 152
|
syl5eq |
|
154 |
148 153
|
sseqtrrd |
|
155 |
|
unieq |
|
156 |
155
|
sseq2d |
|
157 |
156
|
rspcev |
|
158 |
82 154 157
|
syl2anc |
|
159 |
158
|
3exp2 |
|
160 |
159
|
rexlimdv |
|
161 |
63 160
|
syl5bi |
|
162 |
161
|
expimpd |
|
163 |
60 162
|
syl5bi |
|
164 |
163
|
rexlimdv |
|
165 |
56 164
|
mpd |
|
166 |
|
oveq2 |
|
167 |
166
|
sseq1d |
|
168 |
167
|
rexbidv |
|
169 |
|
unieq |
|
170 |
169
|
sseq2d |
|
171 |
170
|
cbvrexvw |
|
172 |
59 171
|
bitrdi |
|
173 |
172
|
cbvrabv |
|
174 |
4 173
|
eqtri |
|
175 |
168 174
|
elrab2 |
|
176 |
49 165 175
|
sylanbrc |
|
177 |
18 21 24 176
|
suprubd |
|
178 |
177 13
|
breqtrrdi |
|
179 |
|
iftrue |
|
180 |
14 179
|
syl5eq |
|
181 |
180
|
breq1d |
|
182 |
178 181
|
syl5ibcom |
|
183 |
32 182
|
mtod |
|
184 |
|
iffalse |
|
185 |
14 184
|
syl5eq |
|
186 |
183 185
|
syl |
|
187 |
186 176
|
eqeltrrd |
|