Step |
Hyp |
Ref |
Expression |
1 |
|
isomushgr.v |
|
2 |
|
isomushgr.w |
|
3 |
|
isomushgr.e |
|
4 |
|
isomushgr.k |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
1 2 5 6
|
isomgr |
|
8 |
|
fvex |
|
9 |
|
vex |
|
10 |
|
fvex |
|
11 |
10
|
cnvex |
|
12 |
9 11
|
coex |
|
13 |
8 12
|
coex |
|
14 |
13
|
a1i |
|
15 |
2 6
|
ushgrf |
|
16 |
|
f1f1orn |
|
17 |
15 16
|
syl |
|
18 |
|
edgval |
|
19 |
4 18
|
eqtri |
|
20 |
|
f1oeq3 |
|
21 |
19 20
|
ax-mp |
|
22 |
17 21
|
sylibr |
|
23 |
22
|
ad3antlr |
|
24 |
|
simprl |
|
25 |
1 5
|
ushgrf |
|
26 |
|
f1f1orn |
|
27 |
25 26
|
syl |
|
28 |
|
edgval |
|
29 |
3 28
|
eqtri |
|
30 |
|
f1oeq3 |
|
31 |
29 30
|
ax-mp |
|
32 |
27 31
|
sylibr |
|
33 |
|
f1ocnv |
|
34 |
32 33
|
syl |
|
35 |
34
|
ad3antrrr |
|
36 |
|
f1oco |
|
37 |
24 35 36
|
syl2anc |
|
38 |
|
f1oco |
|
39 |
23 37 38
|
syl2anc |
|
40 |
29
|
eleq2i |
|
41 |
|
f1fn |
|
42 |
25 41
|
syl |
|
43 |
|
fvelrnb |
|
44 |
42 43
|
syl |
|
45 |
44
|
ad3antrrr |
|
46 |
|
fveq2 |
|
47 |
46
|
imaeq2d |
|
48 |
|
2fveq3 |
|
49 |
47 48
|
eqeq12d |
|
50 |
49
|
rspccv |
|
51 |
50
|
ad2antll |
|
52 |
51
|
imp |
|
53 |
|
coass |
|
54 |
53
|
eqcomi |
|
55 |
54
|
fveq1i |
|
56 |
|
dff1o4 |
|
57 |
27 56
|
sylib |
|
58 |
57
|
simprd |
|
59 |
58
|
ad4antr |
|
60 |
|
f1of |
|
61 |
27 60
|
syl |
|
62 |
61
|
ad3antrrr |
|
63 |
62
|
ffvelrnda |
|
64 |
|
fvco2 |
|
65 |
59 63 64
|
syl2anc |
|
66 |
32
|
ad3antrrr |
|
67 |
|
f1ocnvfv1 |
|
68 |
66 67
|
sylan |
|
69 |
68
|
fveq2d |
|
70 |
|
f1ofn |
|
71 |
70
|
ad2antrl |
|
72 |
|
fvco2 |
|
73 |
71 72
|
sylan |
|
74 |
65 69 73
|
3eqtrd |
|
75 |
55 74
|
syl5req |
|
76 |
75
|
ad2antrr |
|
77 |
|
imaeq2 |
|
78 |
77
|
eqcoms |
|
79 |
|
simpr |
|
80 |
78 79
|
sylan9eqr |
|
81 |
|
fveq2 |
|
82 |
81
|
eqcoms |
|
83 |
82
|
adantl |
|
84 |
76 80 83
|
3eqtr4d |
|
85 |
84
|
ex |
|
86 |
52 85
|
mpdan |
|
87 |
86
|
rexlimdva |
|
88 |
45 87
|
sylbid |
|
89 |
40 88
|
syl5bi |
|
90 |
89
|
ralrimiv |
|
91 |
39 90
|
jca |
|
92 |
|
f1oeq1 |
|
93 |
|
fveq1 |
|
94 |
93
|
eqeq2d |
|
95 |
94
|
ralbidv |
|
96 |
92 95
|
anbi12d |
|
97 |
14 91 96
|
spcedv |
|
98 |
97
|
ex |
|
99 |
98
|
exlimdv |
|
100 |
8
|
cnvex |
|
101 |
|
vex |
|
102 |
101 10
|
coex |
|
103 |
100 102
|
coex |
|
104 |
103
|
a1i |
|
105 |
17
|
ad3antlr |
|
106 |
|
f1ocnv |
|
107 |
105 106
|
syl |
|
108 |
|
f1oeq23 |
|
109 |
29 19 108
|
mp2an |
|
110 |
109
|
biimpi |
|
111 |
110
|
ad2antrl |
|
112 |
27
|
ad3antrrr |
|
113 |
|
f1oco |
|
114 |
111 112 113
|
syl2anc |
|
115 |
|
f1oco |
|
116 |
107 114 115
|
syl2anc |
|
117 |
61
|
ad2antrr |
|
118 |
117
|
ffund |
|
119 |
118
|
adantr |
|
120 |
|
fvelrn |
|
121 |
119 120
|
sylan |
|
122 |
29
|
raleqi |
|
123 |
122
|
biimpi |
|
124 |
123
|
ad2antll |
|
125 |
124
|
adantr |
|
126 |
|
imaeq2 |
|
127 |
|
fveq2 |
|
128 |
126 127
|
eqeq12d |
|
129 |
128
|
rspccva |
|
130 |
125 129
|
sylan |
|
131 |
|
feq3 |
|
132 |
29 131
|
ax-mp |
|
133 |
61 132
|
sylibr |
|
134 |
133
|
ad2antrr |
|
135 |
|
f1ofn |
|
136 |
135
|
adantr |
|
137 |
134 136
|
anim12ci |
|
138 |
137
|
ad2antrr |
|
139 |
|
fnfco |
|
140 |
138 139
|
syl |
|
141 |
|
simplr |
|
142 |
|
fvco2 |
|
143 |
140 141 142
|
syl2anc |
|
144 |
|
f1of |
|
145 |
22 144
|
syl |
|
146 |
145
|
ffund |
|
147 |
|
funcocnv2 |
|
148 |
146 147
|
syl |
|
149 |
148
|
eqcomd |
|
150 |
149
|
ad5antlr |
|
151 |
150
|
coeq1d |
|
152 |
151
|
fveq1d |
|
153 |
|
coass |
|
154 |
153
|
fveq1i |
|
155 |
152 154
|
eqtrdi |
|
156 |
|
f1of |
|
157 |
|
eqid |
|
158 |
157 19
|
feq23i |
|
159 |
156 158
|
sylib |
|
160 |
159
|
adantr |
|
161 |
|
f1of |
|
162 |
32 161
|
syl |
|
163 |
162
|
ad2antrr |
|
164 |
|
fco |
|
165 |
160 163 164
|
syl2anr |
|
166 |
165
|
anim1i |
|
167 |
166
|
adantr |
|
168 |
|
ffvelrn |
|
169 |
167 168
|
syl |
|
170 |
|
fvresi |
|
171 |
169 170
|
syl |
|
172 |
162
|
ad3antrrr |
|
173 |
172
|
anim1i |
|
174 |
173
|
adantr |
|
175 |
|
fvco3 |
|
176 |
174 175
|
syl |
|
177 |
171 176
|
eqtrd |
|
178 |
143 155 177
|
3eqtr3rd |
|
179 |
|
dff1o4 |
|
180 |
22 179
|
sylib |
|
181 |
180
|
simprd |
|
182 |
181
|
ad5antlr |
|
183 |
156
|
adantr |
|
184 |
134 183
|
anim12ci |
|
185 |
184
|
ad2antrr |
|
186 |
|
fco |
|
187 |
185 186
|
syl |
|
188 |
|
fnfco |
|
189 |
182 187 188
|
syl2anc |
|
190 |
|
fvco2 |
|
191 |
189 141 190
|
syl2anc |
|
192 |
130 178 191
|
3eqtrd |
|
193 |
121 192
|
mpdan |
|
194 |
193
|
ralrimiva |
|
195 |
116 194
|
jca |
|
196 |
|
f1oeq1 |
|
197 |
|
fveq1 |
|
198 |
197
|
fveq2d |
|
199 |
198
|
eqeq2d |
|
200 |
199
|
ralbidv |
|
201 |
196 200
|
anbi12d |
|
202 |
104 195 201
|
spcedv |
|
203 |
202
|
ex |
|
204 |
203
|
exlimdv |
|
205 |
99 204
|
impbid |
|
206 |
205
|
pm5.32da |
|
207 |
206
|
exbidv |
|
208 |
7 207
|
bitrd |
|