Step |
Hyp |
Ref |
Expression |
1 |
|
ablfac.b |
|
2 |
|
ablfac.c |
|
3 |
|
ablfac.1 |
|
4 |
|
ablfac.2 |
|
5 |
|
ablfac.o |
|
6 |
|
ablfac.a |
|
7 |
|
ablfac.s |
|
8 |
|
ablfac.w |
|
9 |
|
fzfid |
|
10 |
|
prmnn |
|
11 |
10
|
3ad2ant2 |
|
12 |
|
prmz |
|
13 |
|
ablgrp |
|
14 |
1
|
grpbn0 |
|
15 |
3 13 14
|
3syl |
|
16 |
|
hashnncl |
|
17 |
4 16
|
syl |
|
18 |
15 17
|
mpbird |
|
19 |
|
dvdsle |
|
20 |
12 18 19
|
syl2anr |
|
21 |
20
|
3impia |
|
22 |
18
|
nnzd |
|
23 |
22
|
3ad2ant1 |
|
24 |
|
fznn |
|
25 |
23 24
|
syl |
|
26 |
11 21 25
|
mpbir2and |
|
27 |
26
|
rabssdv |
|
28 |
6 27
|
eqsstrid |
|
29 |
9 28
|
ssfid |
|
30 |
|
dfin5 |
|
31 |
6
|
ssrab3 |
|
32 |
31
|
a1i |
|
33 |
1 5 7 3 4 32
|
ablfac1b |
|
34 |
1
|
fvexi |
|
35 |
34
|
rabex |
|
36 |
35 7
|
dmmpti |
|
37 |
36
|
a1i |
|
38 |
33 37
|
dprdf2 |
|
39 |
38
|
ffvelrnda |
|
40 |
1 2 3 4 5 6 7 8
|
ablfaclem1 |
|
41 |
39 40
|
syl |
|
42 |
|
ssrab2 |
|
43 |
41 42
|
eqsstrdi |
|
44 |
|
sseqin2 |
|
45 |
43 44
|
sylib |
|
46 |
30 45
|
syl5eqr |
|
47 |
46 41
|
eqtrd |
|
48 |
|
eqid |
|
49 |
|
eqid |
|
50 |
|
eqid |
|
51 |
50
|
subgabl |
|
52 |
3 39 51
|
syl2an2r |
|
53 |
32
|
sselda |
|
54 |
50
|
subgbas |
|
55 |
39 54
|
syl |
|
56 |
55
|
fveq2d |
|
57 |
1 5 7 3 4 32
|
ablfac1a |
|
58 |
56 57
|
eqtr3d |
|
59 |
58
|
oveq2d |
|
60 |
18
|
adantr |
|
61 |
53 60
|
pccld |
|
62 |
61
|
nn0zd |
|
63 |
|
pcid |
|
64 |
53 62 63
|
syl2anc |
|
65 |
59 64
|
eqtrd |
|
66 |
65
|
oveq2d |
|
67 |
58 66
|
eqtr4d |
|
68 |
50
|
subggrp |
|
69 |
39 68
|
syl |
|
70 |
4
|
adantr |
|
71 |
1
|
subgss |
|
72 |
39 71
|
syl |
|
73 |
70 72
|
ssfid |
|
74 |
55 73
|
eqeltrrd |
|
75 |
48
|
pgpfi2 |
|
76 |
69 74 75
|
syl2anc |
|
77 |
53 67 76
|
mpbir2and |
|
78 |
48 49 52 77 74
|
pgpfac |
|
79 |
|
ssrab2 |
|
80 |
|
sswrd |
|
81 |
79 80
|
ax-mp |
|
82 |
81
|
sseli |
|
83 |
39
|
adantr |
|
84 |
83
|
adantr |
|
85 |
50
|
subgdmdprd |
|
86 |
83 85
|
syl |
|
87 |
86
|
simprbda |
|
88 |
86
|
simplbda |
|
89 |
50 84 87 88
|
subgdprd |
|
90 |
55
|
ad2antrr |
|
91 |
90
|
eqcomd |
|
92 |
89 91
|
eqeq12d |
|
93 |
92
|
biimpd |
|
94 |
93 87
|
jctild |
|
95 |
94
|
expimpd |
|
96 |
82 95
|
sylan2 |
|
97 |
|
oveq2 |
|
98 |
97
|
eleq1d |
|
99 |
98
|
cbvrabv |
|
100 |
50
|
subsubg |
|
101 |
39 100
|
syl |
|
102 |
101
|
simprbda |
|
103 |
102
|
3adant3 |
|
104 |
39
|
3ad2ant1 |
|
105 |
101
|
simplbda |
|
106 |
105
|
3adant3 |
|
107 |
|
ressabs |
|
108 |
104 106 107
|
syl2anc |
|
109 |
|
simp3 |
|
110 |
108 109
|
eqeltrrd |
|
111 |
|
oveq2 |
|
112 |
111
|
eleq1d |
|
113 |
112 2
|
elrab2 |
|
114 |
103 110 113
|
sylanbrc |
|
115 |
114
|
rabssdv |
|
116 |
99 115
|
eqsstrid |
|
117 |
|
sswrd |
|
118 |
116 117
|
syl |
|
119 |
118
|
sselda |
|
120 |
96 119
|
jctild |
|
121 |
120
|
expimpd |
|
122 |
121
|
reximdv2 |
|
123 |
78 122
|
mpd |
|
124 |
|
rabn0 |
|
125 |
123 124
|
sylibr |
|
126 |
47 125
|
eqnetrd |
|
127 |
|
rabn0 |
|
128 |
126 127
|
sylib |
|
129 |
128
|
ralrimiva |
|
130 |
|
eleq1 |
|
131 |
130
|
ac6sfi |
|
132 |
29 129 131
|
syl2anc |
|
133 |
|
sneq |
|
134 |
|
fveq2 |
|
135 |
134
|
dmeqd |
|
136 |
133 135
|
xpeq12d |
|
137 |
136
|
cbviunv |
|
138 |
|
snfi |
|
139 |
|
simprl |
|
140 |
139
|
ffvelrnda |
|
141 |
|
wrdf |
|
142 |
|
fdm |
|
143 |
140 141 142
|
3syl |
|
144 |
|
fzofi |
|
145 |
143 144
|
eqeltrdi |
|
146 |
|
xpfi |
|
147 |
138 145 146
|
sylancr |
|
148 |
147
|
ralrimiva |
|
149 |
|
iunfi |
|
150 |
29 148 149
|
syl2an2r |
|
151 |
137 150
|
eqeltrid |
|
152 |
|
hashcl |
|
153 |
|
hashfzo0 |
|
154 |
151 152 153
|
3syl |
|
155 |
|
fzofi |
|
156 |
|
hashen |
|
157 |
155 151 156
|
sylancr |
|
158 |
154 157
|
mpbid |
|
159 |
|
bren |
|
160 |
158 159
|
sylib |
|
161 |
3
|
adantr |
|
162 |
4
|
adantr |
|
163 |
|
breq1 |
|
164 |
163
|
cbvrabv |
|
165 |
6 164
|
eqtri |
|
166 |
|
fveq2 |
|
167 |
166
|
breq1d |
|
168 |
167
|
cbvrabv |
|
169 |
|
id |
|
170 |
|
oveq1 |
|
171 |
169 170
|
oveq12d |
|
172 |
171
|
breq2d |
|
173 |
172
|
rabbidv |
|
174 |
168 173
|
syl5eq |
|
175 |
174
|
cbvmptv |
|
176 |
7 175
|
eqtri |
|
177 |
|
breq2 |
|
178 |
|
oveq2 |
|
179 |
178
|
eqeq1d |
|
180 |
177 179
|
anbi12d |
|
181 |
180
|
cbvrabv |
|
182 |
181
|
mpteq2i |
|
183 |
8 182
|
eqtri |
|
184 |
|
simprll |
|
185 |
|
simprlr |
|
186 |
|
2fveq3 |
|
187 |
134 186
|
eleq12d |
|
188 |
187
|
cbvralvw |
|
189 |
185 188
|
sylib |
|
190 |
|
simprr |
|
191 |
1 2 161 162 5 165 176 183 184 189 137 190
|
ablfaclem2 |
|
192 |
191
|
expr |
|
193 |
192
|
exlimdv |
|
194 |
160 193
|
mpd |
|
195 |
132 194
|
exlimddv |
|