Step |
Hyp |
Ref |
Expression |
1 |
|
islindf4.b |
|
2 |
|
islindf4.r |
|
3 |
|
islindf4.t |
|
4 |
|
islindf4.z |
|
5 |
|
islindf4.y |
|
6 |
|
islindf4.l |
|
7 |
|
raldifsni |
|
8 |
|
simpll1 |
|
9 |
|
simprll |
|
10 |
|
ffvelrn |
|
11 |
10
|
3ad2antl3 |
|
12 |
11
|
adantr |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
1 2 3 13 14 15
|
lmodvsinv |
|
17 |
8 9 12 16
|
syl3anc |
|
18 |
17
|
eqeq1d |
|
19 |
|
lmodgrp |
|
20 |
8 19
|
syl |
|
21 |
1 2 3 15
|
lmodvscl |
|
22 |
8 9 12 21
|
syl3anc |
|
23 |
|
lmodcmn |
|
24 |
8 23
|
syl |
|
25 |
|
simpll2 |
|
26 |
|
difexg |
|
27 |
25 26
|
syl |
|
28 |
|
simprlr |
|
29 |
|
elmapi |
|
30 |
28 29
|
syl |
|
31 |
|
simpll3 |
|
32 |
|
difss |
|
33 |
|
fssres |
|
34 |
31 32 33
|
sylancl |
|
35 |
2 15 3 1 8 30 34 27
|
lcomf |
|
36 |
|
simprr |
|
37 |
2 15 3 1 8 30 34 27 4 5 36
|
lcomfsupp |
|
38 |
1 4 24 27 35 37
|
gsumcl |
|
39 |
|
eqid |
|
40 |
1 39 4 13
|
grpinvid2 |
|
41 |
20 22 38 40
|
syl3anc |
|
42 |
|
simplr |
|
43 |
|
fsnunf2 |
|
44 |
30 42 9 43
|
syl3anc |
|
45 |
2 15 3 1 8 44 31 25
|
lcomf |
|
46 |
|
simpr |
|
47 |
|
simpl |
|
48 |
46 47
|
anim12i |
|
49 |
|
elmapfun |
|
50 |
|
fdm |
|
51 |
|
neldifsnd |
|
52 |
|
df-nel |
|
53 |
|
eleq2 |
|
54 |
53
|
notbid |
|
55 |
52 54
|
syl5bb |
|
56 |
51 55
|
mpbird |
|
57 |
29 50 56
|
3syl |
|
58 |
49 57
|
jca |
|
59 |
58
|
adantl |
|
60 |
59
|
adantl |
|
61 |
48 60
|
jca |
|
62 |
|
funsnfsupp |
|
63 |
62
|
bicomd |
|
64 |
61 63
|
syl |
|
65 |
64
|
biimpd |
|
66 |
65
|
impr |
|
67 |
2 15 3 1 8 44 31 25 4 5 66
|
lcomfsupp |
|
68 |
|
incom |
|
69 |
|
disjdif |
|
70 |
68 69
|
eqtri |
|
71 |
70
|
a1i |
|
72 |
|
difsnid |
|
73 |
72
|
eqcomd |
|
74 |
42 73
|
syl |
|
75 |
1 4 39 24 25 45 67 71 74
|
gsumsplit |
|
76 |
|
vex |
|
77 |
|
snex |
|
78 |
76 77
|
unex |
|
79 |
|
simpl3 |
|
80 |
|
simpl2 |
|
81 |
|
fex |
|
82 |
79 80 81
|
syl2anc |
|
83 |
82
|
adantr |
|
84 |
|
offres |
|
85 |
78 83 84
|
sylancr |
|
86 |
30
|
ffnd |
|
87 |
|
neldifsn |
|
88 |
|
fsnunres |
|
89 |
86 87 88
|
sylancl |
|
90 |
89
|
oveq1d |
|
91 |
85 90
|
eqtrd |
|
92 |
91
|
oveq2d |
|
93 |
45
|
ffnd |
|
94 |
|
fnressn |
|
95 |
93 42 94
|
syl2anc |
|
96 |
44
|
ffnd |
|
97 |
31
|
ffnd |
|
98 |
|
fnfvof |
|
99 |
96 97 25 42 98
|
syl22anc |
|
100 |
|
fndm |
|
101 |
100
|
eleq2d |
|
102 |
87 101
|
mtbiri |
|
103 |
|
vex |
|
104 |
|
vex |
|
105 |
|
fsnunfv |
|
106 |
103 104 105
|
mp3an12 |
|
107 |
86 102 106
|
3syl |
|
108 |
107
|
oveq1d |
|
109 |
99 108
|
eqtrd |
|
110 |
109
|
opeq2d |
|
111 |
110
|
sneqd |
|
112 |
|
ovex |
|
113 |
|
fmptsn |
|
114 |
103 112 113
|
mp2an |
|
115 |
114
|
a1i |
|
116 |
95 111 115
|
3eqtrd |
|
117 |
116
|
oveq2d |
|
118 |
|
cmnmnd |
|
119 |
8 23 118
|
3syl |
|
120 |
103
|
a1i |
|
121 |
|
eqidd |
|
122 |
1 121
|
gsumsn |
|
123 |
119 120 22 122
|
syl3anc |
|
124 |
117 123
|
eqtrd |
|
125 |
92 124
|
oveq12d |
|
126 |
75 125
|
eqtr2d |
|
127 |
126
|
eqeq1d |
|
128 |
18 41 127
|
3bitrd |
|
129 |
107
|
eqcomd |
|
130 |
129
|
eqeq1d |
|
131 |
128 130
|
imbi12d |
|
132 |
131
|
anassrs |
|
133 |
132
|
pm5.74da |
|
134 |
|
impexp |
|
135 |
134
|
a1i |
|
136 |
64
|
bicomd |
|
137 |
136
|
imbi1d |
|
138 |
133 135 137
|
3bitr4d |
|
139 |
138
|
2ralbidva |
|
140 |
|
breq1 |
|
141 |
|
oveq1 |
|
142 |
141
|
oveq2d |
|
143 |
142
|
eqeq1d |
|
144 |
|
fveq1 |
|
145 |
144
|
eqeq1d |
|
146 |
143 145
|
imbi12d |
|
147 |
140 146
|
imbi12d |
|
148 |
147
|
ralxpmap |
|
149 |
148
|
adantl |
|
150 |
139 149
|
bitr4d |
|
151 |
|
breq1 |
|
152 |
151
|
ralrab |
|
153 |
150 152
|
syl6bbr |
|
154 |
|
resima |
|
155 |
154
|
eqcomi |
|
156 |
155
|
fveq2i |
|
157 |
156
|
eleq2i |
|
158 |
|
eqid |
|
159 |
79 32 33
|
sylancl |
|
160 |
|
simpl1 |
|
161 |
26
|
3ad2ant2 |
|
162 |
161
|
adantr |
|
163 |
158 1 15 2 5 3 159 160 162
|
ellspd |
|
164 |
157 163
|
syl5bb |
|
165 |
164
|
imbi1d |
|
166 |
|
r19.23v |
|
167 |
165 166
|
syl6bbr |
|
168 |
167
|
ralbidv |
|
169 |
2
|
fvexi |
|
170 |
|
eqid |
|
171 |
|
eqid |
|
172 |
170 15 5 171
|
frlmbas |
|
173 |
169 172
|
mpan |
|
174 |
173
|
3ad2ant2 |
|
175 |
174
|
adantr |
|
176 |
6 175
|
eqtr4id |
|
177 |
176
|
raleqdv |
|
178 |
153 168 177
|
3bitr4d |
|
179 |
7 178
|
syl5bb |
|
180 |
2
|
lmodfgrp |
|
181 |
15 5 14
|
grpinvnzcl |
|
182 |
180 181
|
sylan |
|
183 |
15 5 14
|
grpinvnzcl |
|
184 |
180 183
|
sylan |
|
185 |
|
eldifi |
|
186 |
15 14
|
grpinvinv |
|
187 |
180 185 186
|
syl2an |
|
188 |
187
|
eqcomd |
|
189 |
|
fveq2 |
|
190 |
189
|
rspceeqv |
|
191 |
184 188 190
|
syl2anc |
|
192 |
|
oveq1 |
|
193 |
192
|
eleq1d |
|
194 |
193
|
notbid |
|
195 |
194
|
adantl |
|
196 |
182 191 195
|
ralxfrd |
|
197 |
196
|
3ad2ant1 |
|
198 |
197
|
adantr |
|
199 |
|
simplr |
|
200 |
5
|
fvexi |
|
201 |
200
|
fvconst2 |
|
202 |
199 201
|
syl |
|
203 |
202
|
eqeq2d |
|
204 |
203
|
imbi2d |
|
205 |
204
|
ralbidva |
|
206 |
179 198 205
|
3bitr4d |
|
207 |
206
|
ralbidva |
|
208 |
1 3 158 2 15 5
|
islindf2 |
|
209 |
170 15 6
|
frlmbasf |
|
210 |
209
|
3ad2antl2 |
|
211 |
210
|
ffnd |
|
212 |
|
fnconstg |
|
213 |
200 212
|
ax-mp |
|
214 |
|
eqfnfv |
|
215 |
211 213 214
|
sylancl |
|
216 |
215
|
imbi2d |
|
217 |
216
|
ralbidva |
|
218 |
|
r19.21v |
|
219 |
218
|
ralbii |
|
220 |
|
ralcom |
|
221 |
219 220
|
bitr3i |
|
222 |
217 221
|
syl6bb |
|
223 |
207 208 222
|
3bitr4d |
|