Step |
Hyp |
Ref |
Expression |
1 |
|
derang.d |
|
2 |
|
subfac.n |
|
3 |
|
subfacp1lem.a |
|
4 |
|
subfacp1lem1.n |
|
5 |
|
subfacp1lem1.m |
|
6 |
|
subfacp1lem1.x |
|
7 |
|
subfacp1lem1.k |
|
8 |
|
subfacp1lem3.b |
|
9 |
|
subfacp1lem3.c |
|
10 |
|
fzfi |
|
11 |
|
deranglem |
|
12 |
10 11
|
ax-mp |
|
13 |
3 12
|
eqeltri |
|
14 |
8
|
ssrab3 |
|
15 |
|
ssfi |
|
16 |
13 14 15
|
mp2an |
|
17 |
16
|
elexi |
|
18 |
17
|
a1i |
|
19 |
|
eqid |
|
20 |
|
simpr |
|
21 |
|
fveq1 |
|
22 |
21
|
eqeq1d |
|
23 |
|
fveq1 |
|
24 |
23
|
eqeq1d |
|
25 |
22 24
|
anbi12d |
|
26 |
25 8
|
elrab2 |
|
27 |
20 26
|
sylib |
|
28 |
27
|
simpld |
|
29 |
|
vex |
|
30 |
|
f1oeq1 |
|
31 |
|
fveq1 |
|
32 |
31
|
neeq1d |
|
33 |
32
|
ralbidv |
|
34 |
30 33
|
anbi12d |
|
35 |
29 34 3
|
elab2 |
|
36 |
28 35
|
sylib |
|
37 |
36
|
simpld |
|
38 |
|
f1of1 |
|
39 |
|
df-f1 |
|
40 |
39
|
simprbi |
|
41 |
37 38 40
|
3syl |
|
42 |
|
f1ofn |
|
43 |
37 42
|
syl |
|
44 |
|
fnresdm |
|
45 |
|
f1oeq1 |
|
46 |
43 44 45
|
3syl |
|
47 |
37 46
|
mpbird |
|
48 |
|
f1ofo |
|
49 |
47 48
|
syl |
|
50 |
|
ssun2 |
|
51 |
1 2 3 4 5 6 7
|
subfacp1lem1 |
|
52 |
51
|
simp2d |
|
53 |
50 52
|
sseqtrid |
|
54 |
53
|
adantr |
|
55 |
43 54
|
fnssresd |
|
56 |
27
|
simprd |
|
57 |
56
|
simpld |
|
58 |
6
|
prid2 |
|
59 |
57 58
|
eqeltrdi |
|
60 |
56
|
simprd |
|
61 |
|
1ex |
|
62 |
61
|
prid1 |
|
63 |
60 62
|
eqeltrdi |
|
64 |
|
fveq2 |
|
65 |
64
|
eleq1d |
|
66 |
|
fveq2 |
|
67 |
66
|
eleq1d |
|
68 |
61 6 65 67
|
ralpr |
|
69 |
59 63 68
|
sylanbrc |
|
70 |
|
fvres |
|
71 |
70
|
eleq1d |
|
72 |
71
|
ralbiia |
|
73 |
69 72
|
sylibr |
|
74 |
|
ffnfv |
|
75 |
55 73 74
|
sylanbrc |
|
76 |
|
fveqeq2 |
|
77 |
76
|
rspcev |
|
78 |
58 60 77
|
sylancr |
|
79 |
|
fveqeq2 |
|
80 |
79
|
rspcev |
|
81 |
62 57 80
|
sylancr |
|
82 |
|
eqeq2 |
|
83 |
82
|
rexbidv |
|
84 |
|
eqeq2 |
|
85 |
84
|
rexbidv |
|
86 |
61 6 83 85
|
ralpr |
|
87 |
78 81 86
|
sylanbrc |
|
88 |
|
eqcom |
|
89 |
|
fvres |
|
90 |
89
|
eqeq1d |
|
91 |
88 90
|
syl5bb |
|
92 |
91
|
rexbiia |
|
93 |
92
|
ralbii |
|
94 |
87 93
|
sylibr |
|
95 |
|
dffo3 |
|
96 |
75 94 95
|
sylanbrc |
|
97 |
|
resdif |
|
98 |
41 49 96 97
|
syl3anc |
|
99 |
|
uncom |
|
100 |
99 52
|
syl5eq |
|
101 |
|
incom |
|
102 |
51
|
simp1d |
|
103 |
101 102
|
syl5eq |
|
104 |
|
uneqdifeq |
|
105 |
53 103 104
|
syl2anc |
|
106 |
100 105
|
mpbid |
|
107 |
106
|
adantr |
|
108 |
|
reseq2 |
|
109 |
|
f1oeq1 |
|
110 |
108 109
|
syl |
|
111 |
|
f1oeq2 |
|
112 |
|
f1oeq3 |
|
113 |
110 111 112
|
3bitrd |
|
114 |
107 113
|
syl |
|
115 |
98 114
|
mpbid |
|
116 |
|
ssun1 |
|
117 |
116 52
|
sseqtrid |
|
118 |
117
|
adantr |
|
119 |
36
|
simprd |
|
120 |
|
ssralv |
|
121 |
118 119 120
|
sylc |
|
122 |
29
|
resex |
|
123 |
|
f1oeq1 |
|
124 |
|
fveq1 |
|
125 |
|
fvres |
|
126 |
124 125
|
sylan9eq |
|
127 |
126
|
neeq1d |
|
128 |
127
|
ralbidva |
|
129 |
123 128
|
anbi12d |
|
130 |
122 129 9
|
elab2 |
|
131 |
115 121 130
|
sylanbrc |
|
132 |
4
|
adantr |
|
133 |
5
|
adantr |
|
134 |
|
eqid |
|
135 |
|
simpr |
|
136 |
|
vex |
|
137 |
|
f1oeq1 |
|
138 |
|
fveq1 |
|
139 |
138
|
neeq1d |
|
140 |
139
|
ralbidv |
|
141 |
137 140
|
anbi12d |
|
142 |
136 141 9
|
elab2 |
|
143 |
135 142
|
sylib |
|
144 |
143
|
simpld |
|
145 |
1 2 3 132 133 6 7 134 144
|
subfacp1lem2a |
|
146 |
145
|
simp1d |
|
147 |
1 2 3 132 133 6 7 134 144
|
subfacp1lem2b |
|
148 |
143
|
simprd |
|
149 |
148
|
r19.21bi |
|
150 |
147 149
|
eqnetrd |
|
151 |
150
|
ralrimiva |
|
152 |
145
|
simp2d |
|
153 |
|
elfzuz |
|
154 |
|
eluz2b3 |
|
155 |
154
|
simprbi |
|
156 |
5 153 155
|
3syl |
|
157 |
156
|
adantr |
|
158 |
152 157
|
eqnetrd |
|
159 |
145
|
simp3d |
|
160 |
157
|
necomd |
|
161 |
159 160
|
eqnetrd |
|
162 |
|
fveq2 |
|
163 |
|
id |
|
164 |
162 163
|
neeq12d |
|
165 |
|
fveq2 |
|
166 |
|
id |
|
167 |
165 166
|
neeq12d |
|
168 |
61 6 164 167
|
ralpr |
|
169 |
158 161 168
|
sylanbrc |
|
170 |
|
ralunb |
|
171 |
151 169 170
|
sylanbrc |
|
172 |
52
|
adantr |
|
173 |
172
|
raleqdv |
|
174 |
171 173
|
mpbid |
|
175 |
|
prex |
|
176 |
136 175
|
unex |
|
177 |
|
f1oeq1 |
|
178 |
|
fveq1 |
|
179 |
178
|
neeq1d |
|
180 |
179
|
ralbidv |
|
181 |
177 180
|
anbi12d |
|
182 |
176 181 3
|
elab2 |
|
183 |
146 174 182
|
sylanbrc |
|
184 |
152 159
|
jca |
|
185 |
|
fveq1 |
|
186 |
185
|
eqeq1d |
|
187 |
|
fveq1 |
|
188 |
187
|
eqeq1d |
|
189 |
186 188
|
anbi12d |
|
190 |
189 8
|
elrab2 |
|
191 |
183 184 190
|
sylanbrc |
|
192 |
57
|
adantrr |
|
193 |
152
|
adantrl |
|
194 |
192 193
|
eqtr4d |
|
195 |
60
|
adantrr |
|
196 |
159
|
adantrl |
|
197 |
195 196
|
eqtr4d |
|
198 |
|
fveq2 |
|
199 |
198 162
|
eqeq12d |
|
200 |
|
fveq2 |
|
201 |
200 165
|
eqeq12d |
|
202 |
61 6 199 201
|
ralpr |
|
203 |
194 197 202
|
sylanbrc |
|
204 |
203
|
biantrud |
|
205 |
|
ralunb |
|
206 |
204 205
|
bitr4di |
|
207 |
147
|
eqeq2d |
|
208 |
207
|
ralbidva |
|
209 |
208
|
adantrl |
|
210 |
52
|
adantr |
|
211 |
210
|
raleqdv |
|
212 |
206 209 211
|
3bitr3rd |
|
213 |
125
|
eqeq2d |
|
214 |
|
eqcom |
|
215 |
213 214
|
syl6bb |
|
216 |
215
|
ralbiia |
|
217 |
212 216
|
bitr4di |
|
218 |
43
|
adantrr |
|
219 |
146
|
adantrl |
|
220 |
|
f1ofn |
|
221 |
219 220
|
syl |
|
222 |
|
eqfnfv |
|
223 |
218 221 222
|
syl2anc |
|
224 |
144
|
adantrl |
|
225 |
|
f1ofn |
|
226 |
224 225
|
syl |
|
227 |
117
|
adantr |
|
228 |
218 227
|
fnssresd |
|
229 |
|
eqfnfv |
|
230 |
226 228 229
|
syl2anc |
|
231 |
217 223 230
|
3bitr4d |
|
232 |
19 131 191 231
|
f1o2d |
|
233 |
18 232
|
hasheqf1od |
|
234 |
9
|
fveq2i |
|
235 |
|
fzfi |
|
236 |
|
diffi |
|
237 |
235 236
|
ax-mp |
|
238 |
7 237
|
eqeltri |
|
239 |
1
|
derangval |
|
240 |
238 239
|
ax-mp |
|
241 |
1 2
|
derangen2 |
|
242 |
238 241
|
ax-mp |
|
243 |
234 240 242
|
3eqtr2ri |
|
244 |
51
|
simp3d |
|
245 |
244
|
fveq2d |
|
246 |
243 245
|
syl5eqr |
|
247 |
233 246
|
eqtrd |
|