Step |
Hyp |
Ref |
Expression |
1 |
|
frgpup.b |
|
2 |
|
frgpup.n |
|
3 |
|
frgpup.t |
|
4 |
|
frgpup.h |
|
5 |
|
frgpup.i |
|
6 |
|
frgpup.a |
|
7 |
|
frgpup.w |
|
8 |
|
frgpup.r |
|
9 |
7 8
|
efgval |
|
10 |
|
coeq2 |
|
11 |
10
|
oveq2d |
|
12 |
|
eqid |
|
13 |
11 12
|
eqer |
|
14 |
13
|
a1i |
|
15 |
|
ssv |
|
16 |
15
|
a1i |
|
17 |
14 16
|
erinxp |
|
18 |
|
df-xp |
|
19 |
18
|
ineq1i |
|
20 |
|
incom |
|
21 |
|
inopab |
|
22 |
19 20 21
|
3eqtr3i |
|
23 |
|
vex |
|
24 |
|
vex |
|
25 |
23 24
|
prss |
|
26 |
25
|
anbi1i |
|
27 |
26
|
opabbii |
|
28 |
22 27
|
eqtri |
|
29 |
|
ereq1 |
|
30 |
28 29
|
ax-mp |
|
31 |
17 30
|
sylib |
|
32 |
|
simplrl |
|
33 |
|
fviss |
|
34 |
7 33
|
eqsstri |
|
35 |
34 32
|
sseldi |
|
36 |
|
opelxpi |
|
37 |
36
|
adantl |
|
38 |
|
simprl |
|
39 |
|
2oconcl |
|
40 |
39
|
ad2antll |
|
41 |
38 40
|
opelxpd |
|
42 |
37 41
|
s2cld |
|
43 |
|
splcl |
|
44 |
35 42 43
|
syl2anc |
|
45 |
7
|
efgrcl |
|
46 |
32 45
|
syl |
|
47 |
46
|
simprd |
|
48 |
44 47
|
eleqtrrd |
|
49 |
|
pfxcl |
|
50 |
35 49
|
syl |
|
51 |
1 2 3 4 5 6
|
frgpuptf |
|
52 |
51
|
ad2antrr |
|
53 |
|
ccatco |
|
54 |
50 42 52 53
|
syl3anc |
|
55 |
54
|
oveq2d |
|
56 |
4
|
ad2antrr |
|
57 |
|
grpmnd |
|
58 |
56 57
|
syl |
|
59 |
|
wrdco |
|
60 |
50 52 59
|
syl2anc |
|
61 |
|
wrdco |
|
62 |
42 52 61
|
syl2anc |
|
63 |
|
eqid |
|
64 |
1 63
|
gsumccat |
|
65 |
58 60 62 64
|
syl3anc |
|
66 |
52 37 41
|
s2co |
|
67 |
|
df-ov |
|
68 |
67
|
a1i |
|
69 |
67
|
fveq2i |
|
70 |
|
df-ov |
|
71 |
|
eqid |
|
72 |
71
|
efgmval |
|
73 |
70 72
|
syl5eqr |
|
74 |
73
|
adantl |
|
75 |
74
|
fveq2d |
|
76 |
1 2 3 4 5 6 71
|
frgpuptinv |
|
77 |
36 76
|
sylan2 |
|
78 |
77
|
adantlr |
|
79 |
75 78
|
eqtr3d |
|
80 |
69 79
|
eqtr4id |
|
81 |
68 80
|
s2eqd |
|
82 |
66 81
|
eqtr4d |
|
83 |
82
|
oveq2d |
|
84 |
|
simprr |
|
85 |
52 38 84
|
fovrnd |
|
86 |
1 2
|
grpinvcl |
|
87 |
56 85 86
|
syl2anc |
|
88 |
1 63
|
gsumws2 |
|
89 |
58 85 87 88
|
syl3anc |
|
90 |
|
eqid |
|
91 |
1 63 90 2
|
grprinv |
|
92 |
56 85 91
|
syl2anc |
|
93 |
83 89 92
|
3eqtrd |
|
94 |
93
|
oveq2d |
|
95 |
1
|
gsumwcl |
|
96 |
58 60 95
|
syl2anc |
|
97 |
1 63 90
|
grprid |
|
98 |
56 96 97
|
syl2anc |
|
99 |
94 98
|
eqtrd |
|
100 |
55 65 99
|
3eqtrrd |
|
101 |
100
|
oveq1d |
|
102 |
|
swrdcl |
|
103 |
35 102
|
syl |
|
104 |
|
wrdco |
|
105 |
103 52 104
|
syl2anc |
|
106 |
1 63
|
gsumccat |
|
107 |
58 60 105 106
|
syl3anc |
|
108 |
|
ccatcl |
|
109 |
50 42 108
|
syl2anc |
|
110 |
|
wrdco |
|
111 |
109 52 110
|
syl2anc |
|
112 |
1 63
|
gsumccat |
|
113 |
58 111 105 112
|
syl3anc |
|
114 |
101 107 113
|
3eqtr4d |
|
115 |
|
simplrr |
|
116 |
|
lencl |
|
117 |
35 116
|
syl |
|
118 |
|
nn0uz |
|
119 |
117 118
|
eleqtrdi |
|
120 |
|
eluzfz2 |
|
121 |
119 120
|
syl |
|
122 |
|
ccatpfx |
|
123 |
35 115 121 122
|
syl3anc |
|
124 |
|
pfxid |
|
125 |
35 124
|
syl |
|
126 |
123 125
|
eqtrd |
|
127 |
126
|
coeq2d |
|
128 |
|
ccatco |
|
129 |
50 103 52 128
|
syl3anc |
|
130 |
127 129
|
eqtr3d |
|
131 |
130
|
oveq2d |
|
132 |
|
splval |
|
133 |
32 115 115 42 132
|
syl13anc |
|
134 |
133
|
coeq2d |
|
135 |
|
ccatco |
|
136 |
109 103 52 135
|
syl3anc |
|
137 |
134 136
|
eqtrd |
|
138 |
137
|
oveq2d |
|
139 |
114 131 138
|
3eqtr4d |
|
140 |
|
vex |
|
141 |
|
ovex |
|
142 |
|
eleq1 |
|
143 |
|
eleq1 |
|
144 |
142 143
|
bi2anan9 |
|
145 |
25 144
|
bitr3id |
|
146 |
|
coeq2 |
|
147 |
146
|
oveq2d |
|
148 |
|
coeq2 |
|
149 |
148
|
oveq2d |
|
150 |
147 149
|
eqeqan12d |
|
151 |
145 150
|
anbi12d |
|
152 |
|
eqid |
|
153 |
140 141 151 152
|
braba |
|
154 |
32 48 139 153
|
syl21anbrc |
|
155 |
154
|
ralrimivva |
|
156 |
155
|
ralrimivva |
|
157 |
7
|
fvexi |
|
158 |
|
erex |
|
159 |
31 157 158
|
mpisyl |
|
160 |
|
ereq1 |
|
161 |
|
breq |
|
162 |
161
|
2ralbidv |
|
163 |
162
|
2ralbidv |
|
164 |
160 163
|
anbi12d |
|
165 |
164
|
elabg |
|
166 |
159 165
|
syl |
|
167 |
31 156 166
|
mpbir2and |
|
168 |
|
intss1 |
|
169 |
167 168
|
syl |
|
170 |
9 169
|
eqsstrid |
|
171 |
170
|
ssbrd |
|
172 |
171
|
imp |
|
173 |
7 8
|
efger |
|
174 |
|
errel |
|
175 |
173 174
|
mp1i |
|
176 |
|
brrelex12 |
|
177 |
175 176
|
sylan |
|
178 |
|
preq12 |
|
179 |
178
|
sseq1d |
|
180 |
|
coeq2 |
|
181 |
180
|
oveq2d |
|
182 |
|
coeq2 |
|
183 |
182
|
oveq2d |
|
184 |
181 183
|
eqeqan12d |
|
185 |
179 184
|
anbi12d |
|
186 |
185 152
|
brabga |
|
187 |
177 186
|
syl |
|
188 |
172 187
|
mpbid |
|
189 |
188
|
simprd |
|