Step |
Hyp |
Ref |
Expression |
1 |
|
yoneda.y |
|
2 |
|
yoneda.b |
|
3 |
|
yoneda.1 |
|
4 |
|
yoneda.o |
|
5 |
|
yoneda.s |
|
6 |
|
yoneda.t |
|
7 |
|
yoneda.q |
|
8 |
|
yoneda.h |
|
9 |
|
yoneda.r |
|
10 |
|
yoneda.e |
|
11 |
|
yoneda.z |
|
12 |
|
yoneda.c |
|
13 |
|
yoneda.w |
|
14 |
|
yoneda.u |
|
15 |
|
yoneda.v |
|
16 |
|
yoneda.m |
|
17 |
|
yonedainv.i |
|
18 |
|
yonedainv.n |
|
19 |
|
relfunc |
|
20 |
15
|
unssbd |
|
21 |
13 20
|
ssexd |
|
22 |
1 12 4 5 7 21 14
|
yoncl |
|
23 |
|
1st2nd |
|
24 |
19 22 23
|
sylancr |
|
25 |
|
1st2ndbr |
|
26 |
19 22 25
|
sylancr |
|
27 |
|
fveq2 |
|
28 |
|
df-ov |
|
29 |
27 28
|
eqtr4di |
|
30 |
|
fveq2 |
|
31 |
|
df-ov |
|
32 |
30 31
|
eqtr4di |
|
33 |
|
fveq2 |
|
34 |
|
df-ov |
|
35 |
33 34
|
eqtr4di |
|
36 |
32 35
|
oveq12d |
|
37 |
29 36
|
eleq12d |
|
38 |
9
|
fucbas |
|
39 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
|
yonedalem1 |
|
40 |
39
|
simpld |
|
41 |
|
funcrcl |
|
42 |
40 41
|
syl |
|
43 |
42
|
simpld |
|
44 |
42
|
simprd |
|
45 |
9 43 44
|
fuccat |
|
46 |
39
|
simprd |
|
47 |
|
eqid |
|
48 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
|
yonedainv |
|
49 |
38 17 45 40 46 47 48
|
inviso2 |
|
50 |
|
eqid |
|
51 |
7
|
fucbas |
|
52 |
4 2
|
oppcbas |
|
53 |
50 51 52
|
xpcbas |
|
54 |
|
eqid |
|
55 |
|
eqid |
|
56 |
9 53 54 46 40 47 55
|
fuciso |
|
57 |
49 56
|
mpbid |
|
58 |
57
|
simprd |
|
59 |
58
|
adantr |
|
60 |
2 51 26
|
funcf1 |
|
61 |
60
|
adantr |
|
62 |
|
simprr |
|
63 |
61 62
|
ffvelrnd |
|
64 |
|
simprl |
|
65 |
63 64
|
opelxpd |
|
66 |
37 59 65
|
rspcdva |
|
67 |
4
|
oppccat |
|
68 |
12 67
|
syl |
|
69 |
68
|
adantr |
|
70 |
5
|
setccat |
|
71 |
21 70
|
syl |
|
72 |
71
|
adantr |
|
73 |
10 69 72 52 63 64
|
evlf1 |
|
74 |
12
|
adantr |
|
75 |
|
eqid |
|
76 |
1 2 74 62 75 64
|
yon11 |
|
77 |
73 76
|
eqtrd |
|
78 |
13
|
adantr |
|
79 |
14
|
adantr |
|
80 |
15
|
adantr |
|
81 |
1 2 3 4 5 6 7 8 9 10 11 74 78 79 80 63 64
|
yonedalem21 |
|
82 |
77 81
|
oveq12d |
|
83 |
66 82
|
eleqtrd |
|
84 |
20
|
adantr |
|
85 |
|
eqid |
|
86 |
|
relfunc |
|
87 |
|
1st2ndbr |
|
88 |
86 63 87
|
sylancr |
|
89 |
52 85 88
|
funcf1 |
|
90 |
89 64
|
ffvelrnd |
|
91 |
5 21
|
setcbas |
|
92 |
91
|
adantr |
|
93 |
90 92
|
eleqtrrd |
|
94 |
76 93
|
eqeltrrd |
|
95 |
84 94
|
sseldd |
|
96 |
|
eqid |
|
97 |
|
eqid |
|
98 |
7 97
|
fuchom |
|
99 |
61 64
|
ffvelrnd |
|
100 |
96 51 98 99 63
|
homfval |
|
101 |
15
|
unssad |
|
102 |
101
|
adantr |
|
103 |
96 51
|
homffn |
|
104 |
|
fnovrn |
|
105 |
103 99 63 104
|
mp3an2i |
|
106 |
102 105
|
sseldd |
|
107 |
100 106
|
eqeltrrd |
|
108 |
6 78 95 107 55
|
setciso |
|
109 |
83 108
|
mpbid |
|
110 |
74
|
adantr |
|
111 |
110
|
adantr |
|
112 |
64
|
adantr |
|
113 |
112
|
adantr |
|
114 |
|
simpr |
|
115 |
1 2 111 113 75 114
|
yon11 |
|
116 |
115
|
eqcomd |
|
117 |
111
|
adantr |
|
118 |
62
|
ad3antrrr |
|
119 |
113
|
adantr |
|
120 |
|
eqid |
|
121 |
114
|
adantr |
|
122 |
|
simpr |
|
123 |
|
simpllr |
|
124 |
1 2 117 118 75 119 120 121 122 123
|
yon12 |
|
125 |
1 2 117 119 75 118 120 121 123 122
|
yon2 |
|
126 |
124 125
|
eqtr4d |
|
127 |
116 126
|
mpteq12dva |
|
128 |
26
|
adantr |
|
129 |
2 75 98 128 64 62
|
funcf2 |
|
130 |
129
|
ffvelrnda |
|
131 |
97 130
|
nat1st2nd |
|
132 |
131
|
adantr |
|
133 |
|
eqid |
|
134 |
97 132 52 133 114
|
natcl |
|
135 |
21
|
adantr |
|
136 |
135
|
ad2antrr |
|
137 |
60
|
ad2antrr |
|
138 |
137 112
|
ffvelrnd |
|
139 |
|
1st2ndbr |
|
140 |
86 138 139
|
sylancr |
|
141 |
52 85 140
|
funcf1 |
|
142 |
141
|
ffvelrnda |
|
143 |
92
|
ad2antrr |
|
144 |
142 143
|
eleqtrrd |
|
145 |
89
|
adantr |
|
146 |
145
|
ffvelrnda |
|
147 |
146 143
|
eleqtrrd |
|
148 |
5 136 133 144 147
|
elsetchom |
|
149 |
134 148
|
mpbid |
|
150 |
149
|
feqmptd |
|
151 |
127 150
|
eqtr4d |
|
152 |
151
|
mpteq2dva |
|
153 |
78
|
adantr |
|
154 |
79
|
adantr |
|
155 |
80
|
adantr |
|
156 |
63
|
adantr |
|
157 |
76
|
eleq2d |
|
158 |
157
|
biimpar |
|
159 |
1 2 3 4 5 6 7 8 9 10 11 110 153 154 155 156 112 18 158
|
yonedalem4a |
|
160 |
97 131 52
|
natfn |
|
161 |
|
dffn5 |
|
162 |
160 161
|
sylib |
|
163 |
152 159 162
|
3eqtr4d |
|
164 |
163
|
mpteq2dva |
|
165 |
|
f1of |
|
166 |
109 165
|
syl |
|
167 |
166
|
feqmptd |
|
168 |
129
|
feqmptd |
|
169 |
164 167 168
|
3eqtr4d |
|
170 |
|
f1oeq1 |
|
171 |
169 170
|
syl |
|
172 |
109 171
|
mpbid |
|
173 |
172
|
ralrimivva |
|
174 |
2 75 98
|
isffth2 |
|
175 |
26 173 174
|
sylanbrc |
|
176 |
|
df-br |
|
177 |
175 176
|
sylib |
|
178 |
24 177
|
eqeltrd |
|