Step |
Hyp |
Ref |
Expression |
1 |
|
curf2ndf.q |
|
2 |
|
curf2ndf.c |
|
3 |
|
curf2ndf.d |
|
4 |
|
df-ov |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
5 6 7
|
xpcbas |
|
9 |
|
eqid |
|
10 |
2
|
ad2antrr |
|
11 |
3
|
ad2antrr |
|
12 |
|
eqid |
|
13 |
|
opelxpi |
|
14 |
13
|
adantll |
|
15 |
5 8 9 10 11 12 14
|
2ndf1 |
|
16 |
|
vex |
|
17 |
|
vex |
|
18 |
16 17
|
op2nd |
|
19 |
15 18
|
eqtrdi |
|
20 |
4 19
|
syl5eq |
|
21 |
20
|
mpteq2dva |
|
22 |
|
mptresid |
|
23 |
21 22
|
eqtr4di |
|
24 |
|
df-ov |
|
25 |
10
|
ad2antrr |
|
26 |
11
|
ad2antrr |
|
27 |
14
|
ad2antrr |
|
28 |
|
simp-4r |
|
29 |
|
simplr |
|
30 |
28 29
|
opelxpd |
|
31 |
5 8 9 25 26 12 27 30
|
2ndf2 |
|
32 |
31
|
fveq1d |
|
33 |
24 32
|
syl5eq |
|
34 |
|
eqid |
|
35 |
|
eqid |
|
36 |
2
|
adantr |
|
37 |
|
simpr |
|
38 |
6 34 35 36 37
|
catidcl |
|
39 |
38
|
ad5ant12 |
|
40 |
|
simpr |
|
41 |
39 40
|
opelxpd |
|
42 |
|
eqid |
|
43 |
|
simpllr |
|
44 |
5 6 7 34 42 28 43 28 29 9
|
xpchom2 |
|
45 |
41 44
|
eleqtrrd |
|
46 |
45
|
fvresd |
|
47 |
|
fvex |
|
48 |
|
vex |
|
49 |
47 48
|
op2nd |
|
50 |
46 49
|
eqtrdi |
|
51 |
33 50
|
eqtrd |
|
52 |
51
|
mpteq2dva |
|
53 |
|
mptresid |
|
54 |
52 53
|
eqtr4di |
|
55 |
54
|
3impa |
|
56 |
55
|
mpoeq3dva |
|
57 |
|
fveq2 |
|
58 |
|
df-ov |
|
59 |
57 58
|
eqtr4di |
|
60 |
59
|
reseq2d |
|
61 |
60
|
mpompt |
|
62 |
56 61
|
eqtr4di |
|
63 |
23 62
|
opeq12d |
|
64 |
|
eqid |
|
65 |
3
|
adantr |
|
66 |
5 2 3 12
|
2ndfcl |
|
67 |
66
|
adantr |
|
68 |
|
eqid |
|
69 |
64 6 36 65 67 7 37 68 42 35
|
curf1 |
|
70 |
|
eqid |
|
71 |
70 7 65 42
|
idfuval |
|
72 |
63 69 71
|
3eqtr4d |
|
73 |
|
eqid |
|
74 |
1 3 3
|
fuccat |
|
75 |
74
|
adantr |
|
76 |
1
|
fucbas |
|
77 |
70
|
idfucl |
|
78 |
3 77
|
syl |
|
79 |
78
|
adantr |
|
80 |
|
eqid |
|
81 |
73 75 36 76 79 80 6 37
|
diag11 |
|
82 |
72 81
|
eqtr4d |
|
83 |
82
|
mpteq2dva |
|
84 |
|
relfunc |
|
85 |
64 1 2 3 66
|
curfcl |
|
86 |
|
1st2ndbr |
|
87 |
84 85 86
|
sylancr |
|
88 |
6 76 87
|
funcf1 |
|
89 |
88
|
feqmptd |
|
90 |
73 74 2 76 78 80
|
diag1cl |
|
91 |
|
1st2ndbr |
|
92 |
84 90 91
|
sylancr |
|
93 |
6 76 92
|
funcf1 |
|
94 |
93
|
feqmptd |
|
95 |
83 89 94
|
3eqtr4d |
|
96 |
3
|
ad2antrr |
|
97 |
70 7 96
|
idfu1st |
|
98 |
97
|
coeq2d |
|
99 |
|
eqid |
|
100 |
|
eqid |
|
101 |
78
|
ad2antrr |
|
102 |
1 99 100 101
|
fucid |
|
103 |
7 100
|
cidfn |
|
104 |
96 103
|
syl |
|
105 |
|
dffn2 |
|
106 |
104 105
|
sylib |
|
107 |
106
|
feqmptd |
|
108 |
|
fcoi1 |
|
109 |
106 108
|
syl |
|
110 |
2
|
ad2antrr |
|
111 |
110
|
adantr |
|
112 |
96
|
adantr |
|
113 |
|
simplrl |
|
114 |
|
opelxpi |
|
115 |
113 114
|
sylan |
|
116 |
|
simplrr |
|
117 |
|
opelxpi |
|
118 |
116 117
|
sylan |
|
119 |
5 8 9 111 112 12 115 118
|
2ndf2 |
|
120 |
119
|
oveqd |
|
121 |
|
df-ov |
|
122 |
|
simplr |
|
123 |
|
simpr |
|
124 |
7 42 100 112 123
|
catidcl |
|
125 |
122 124
|
opelxpd |
|
126 |
113
|
adantr |
|
127 |
116
|
adantr |
|
128 |
5 6 7 34 42 126 123 127 123 9
|
xpchom2 |
|
129 |
125 128
|
eleqtrrd |
|
130 |
129
|
fvresd |
|
131 |
121 130
|
syl5eq |
|
132 |
|
fvex |
|
133 |
48 132
|
op2nd |
|
134 |
131 133
|
eqtrdi |
|
135 |
120 134
|
eqtrd |
|
136 |
135
|
mpteq2dva |
|
137 |
107 109 136
|
3eqtr4rd |
|
138 |
98 102 137
|
3eqtr4rd |
|
139 |
66
|
ad2antrr |
|
140 |
|
simpr |
|
141 |
|
eqid |
|
142 |
64 6 110 96 139 7 34 100 113 116 140 141
|
curf2 |
|
143 |
74
|
ad2antrr |
|
144 |
73 143 110 76 101 80 6 113 34 99 116 140
|
diag12 |
|
145 |
138 142 144
|
3eqtr4d |
|
146 |
145
|
mpteq2dva |
|
147 |
|
eqid |
|
148 |
1 147
|
fuchom |
|
149 |
87
|
adantr |
|
150 |
|
simprl |
|
151 |
|
simprr |
|
152 |
6 34 148 149 150 151
|
funcf2 |
|
153 |
152
|
feqmptd |
|
154 |
92
|
adantr |
|
155 |
6 34 148 154 150 151
|
funcf2 |
|
156 |
155
|
feqmptd |
|
157 |
146 153 156
|
3eqtr4d |
|
158 |
157
|
3impb |
|
159 |
158
|
mpoeq3dva |
|
160 |
6 87
|
funcfn2 |
|
161 |
|
fnov |
|
162 |
160 161
|
sylib |
|
163 |
6 92
|
funcfn2 |
|
164 |
|
fnov |
|
165 |
163 164
|
sylib |
|
166 |
159 162 165
|
3eqtr4d |
|
167 |
95 166
|
opeq12d |
|
168 |
|
1st2nd |
|
169 |
84 85 168
|
sylancr |
|
170 |
|
1st2nd |
|
171 |
84 90 170
|
sylancr |
|
172 |
167 169 171
|
3eqtr4d |
|