Step |
Hyp |
Ref |
Expression |
1 |
|
cofsmo.1 |
|
2 |
|
cofsmo.2 |
|
3 |
|
cofsmo.3 |
|
4 |
1
|
ssrab3 |
|
5 |
|
ssexg |
|
6 |
4 5
|
mpan |
|
7 |
|
onss |
|
8 |
4 7
|
sstrid |
|
9 |
|
epweon |
|
10 |
|
wess |
|
11 |
8 9 10
|
mpisyl |
|
12 |
3
|
oiiso |
|
13 |
6 11 12
|
syl2anc |
|
14 |
13
|
ad2antlr |
|
15 |
|
isof1o |
|
16 |
|
f1ofo |
|
17 |
14 15 16
|
3syl |
|
18 |
|
fof |
|
19 |
|
fss |
|
20 |
18 4 19
|
sylancl |
|
21 |
17 20
|
syl |
|
22 |
3
|
oion |
|
23 |
6 22
|
syl |
|
24 |
23
|
ad2antlr |
|
25 |
|
simplr |
|
26 |
|
eloni |
|
27 |
|
smoiso2 |
|
28 |
26 8 27
|
syl2an |
|
29 |
28
|
biimpar |
|
30 |
29
|
simprd |
|
31 |
24 25 14 30
|
syl21anc |
|
32 |
|
eloni |
|
33 |
32
|
ad2antlr |
|
34 |
|
smorndom |
|
35 |
21 31 33 34
|
syl3anc |
|
36 |
|
onsssuc |
|
37 |
24 25 36
|
syl2anc |
|
38 |
35 37
|
mpbid |
|
39 |
38
|
adantrr |
|
40 |
|
vex |
|
41 |
3
|
oiexg |
|
42 |
6 41
|
syl |
|
43 |
42
|
ad2antlr |
|
44 |
|
coexg |
|
45 |
40 43 44
|
sylancr |
|
46 |
|
simprl |
|
47 |
21
|
adantrr |
|
48 |
|
fco |
|
49 |
46 47 48
|
syl2anc |
|
50 |
|
simpr |
|
51 |
50 21 48
|
syl2anc |
|
52 |
|
ordsson |
|
53 |
52
|
ad2antrr |
|
54 |
24 26
|
syl |
|
55 |
17 18
|
syl |
|
56 |
|
simpl |
|
57 |
|
ffvelrn |
|
58 |
55 56 57
|
syl2an |
|
59 |
|
ffn |
|
60 |
17 18 59
|
3syl |
|
61 |
60 31
|
jca |
|
62 |
|
smoel2 |
|
63 |
61 62
|
sylan |
|
64 |
|
fveq2 |
|
65 |
64
|
eleq2d |
|
66 |
65
|
raleqbi1dv |
|
67 |
|
fveq2 |
|
68 |
67
|
eleq1d |
|
69 |
68
|
cbvralvw |
|
70 |
|
fveq2 |
|
71 |
70
|
eleq2d |
|
72 |
71
|
raleqbi1dv |
|
73 |
69 72
|
syl5bb |
|
74 |
73
|
cbvrabv |
|
75 |
1 74
|
eqtri |
|
76 |
66 75
|
elrab2 |
|
77 |
76
|
simprbi |
|
78 |
|
fveq2 |
|
79 |
78
|
eleq1d |
|
80 |
79
|
rspccv |
|
81 |
77 80
|
syl |
|
82 |
58 63 81
|
sylc |
|
83 |
|
ordtr1 |
|
84 |
83
|
ancomsd |
|
85 |
24 26 84
|
3syl |
|
86 |
85
|
imp |
|
87 |
|
fvco3 |
|
88 |
21 86 87
|
syl2an2r |
|
89 |
|
simprl |
|
90 |
|
fvco3 |
|
91 |
21 89 90
|
syl2an2r |
|
92 |
82 88 91
|
3eltr4d |
|
93 |
92
|
ralrimivva |
|
94 |
|
issmo2 |
|
95 |
94
|
imp |
|
96 |
51 53 54 93 95
|
syl13anc |
|
97 |
96
|
adantrr |
|
98 |
|
rabn0 |
|
99 |
|
ssrab2 |
|
100 |
99 7
|
sstrid |
|
101 |
|
fveq2 |
|
102 |
101
|
sseq2d |
|
103 |
102
|
cbvrabv |
|
104 |
103
|
inteqi |
|
105 |
2 104
|
eqtri |
|
106 |
|
onint |
|
107 |
105 106
|
eqeltrid |
|
108 |
100 107
|
sylan |
|
109 |
98 108
|
sylan2br |
|
110 |
|
fveq2 |
|
111 |
110
|
sseq2d |
|
112 |
111
|
elrab |
|
113 |
109 112
|
sylib |
|
114 |
113
|
ex |
|
115 |
114
|
adantl |
|
116 |
|
simpr2 |
|
117 |
|
simp3 |
|
118 |
105
|
eleq2i |
|
119 |
|
simp21 |
|
120 |
|
simp1l |
|
121 |
120 52
|
syl |
|
122 |
119 121
|
fssd |
|
123 |
|
simp22 |
|
124 |
122 123
|
ffvelrnd |
|
125 |
|
simp1r |
|
126 |
|
ontr1 |
|
127 |
126
|
3impib |
|
128 |
125 117 123 127
|
syl3anc |
|
129 |
122 128
|
ffvelrnd |
|
130 |
|
ontri1 |
|
131 |
124 129 130
|
syl2anc |
|
132 |
|
simp23 |
|
133 |
|
simpl1 |
|
134 |
133 100
|
syl |
|
135 |
|
sstr |
|
136 |
127 135
|
anim12i |
|
137 |
|
rabid |
|
138 |
136 137
|
sylibr |
|
139 |
|
onnmin |
|
140 |
134 138 139
|
syl2anc |
|
141 |
140
|
expr |
|
142 |
125 117 123 132 141
|
syl31anc |
|
143 |
131 142
|
sylbird |
|
144 |
143
|
con4d |
|
145 |
118 144
|
syl5bi |
|
146 |
117 145
|
mpd |
|
147 |
146
|
3expia |
|
148 |
147
|
ralrimiv |
|
149 |
|
fveq2 |
|
150 |
149
|
eleq2d |
|
151 |
150
|
raleqbi1dv |
|
152 |
151 1
|
elrab2 |
|
153 |
116 148 152
|
sylanbrc |
|
154 |
153
|
expcom |
|
155 |
154
|
3expib |
|
156 |
155
|
com13 |
|
157 |
115 156
|
syld |
|
158 |
157
|
com23 |
|
159 |
158
|
imp31 |
|
160 |
|
foelrn |
|
161 |
17 159 160
|
syl2an2r |
|
162 |
|
eleq1 |
|
163 |
162
|
biimpcd |
|
164 |
|
fveq2 |
|
165 |
164
|
sseq2d |
|
166 |
67
|
sseq2d |
|
167 |
166
|
cbvrabv |
|
168 |
165 167
|
elrab2 |
|
169 |
168
|
simprbi |
|
170 |
163 169
|
syl6 |
|
171 |
109 170
|
syl |
|
172 |
171
|
ad5ant24 |
|
173 |
21
|
ad2antrr |
|
174 |
|
fvco3 |
|
175 |
173 174
|
sylancom |
|
176 |
175
|
sseq2d |
|
177 |
172 176
|
sylibrd |
|
178 |
177
|
reximdva |
|
179 |
161 178
|
mpd |
|
180 |
179
|
ex |
|
181 |
180
|
ralimdv |
|
182 |
181
|
impr |
|
183 |
49 97 182
|
3jca |
|
184 |
|
feq1 |
|
185 |
|
smoeq |
|
186 |
|
fveq1 |
|
187 |
186
|
sseq2d |
|
188 |
187
|
rexbidv |
|
189 |
188
|
ralbidv |
|
190 |
184 185 189
|
3anbi123d |
|
191 |
45 183 190
|
spcedv |
|
192 |
|
feq2 |
|
193 |
|
rexeq |
|
194 |
193
|
ralbidv |
|
195 |
192 194
|
3anbi13d |
|
196 |
195
|
exbidv |
|
197 |
196
|
rspcev |
|
198 |
39 191 197
|
syl2anc |
|
199 |
198
|
ex |
|
200 |
199
|
exlimdv |
|