Step |
Hyp |
Ref |
Expression |
1 |
|
fuco11.o |
Could not format ( ph -> ( <. C , D >. o.F E ) = <. O , P >. ) : No typesetting found for |- ( ph -> ( <. C , D >. o.F E ) = <. O , P >. ) with typecode |- |
2 |
|
fuco11.f |
|
3 |
|
fuco11.k |
|
4 |
|
fuco11.u |
|
5 |
|
fuco21.m |
|
6 |
|
fuco21.r |
|
7 |
|
fuco21.v |
|
8 |
2
|
funcrcl2 |
|
9 |
3
|
funcrcl2 |
|
10 |
3
|
funcrcl3 |
|
11 |
|
eqidd |
|
12 |
8 9 10 1 11
|
fuco2 |
|
13 |
|
fvexd |
|
14 |
|
simprl |
|
15 |
4
|
adantr |
|
16 |
14 15
|
eqtrd |
|
17 |
16
|
fveq2d |
|
18 |
17
|
fveq2d |
|
19 |
|
opex |
|
20 |
|
opex |
|
21 |
19 20
|
op2nd |
|
22 |
21
|
fveq2i |
|
23 |
|
relfunc |
|
24 |
23
|
brrelex1i |
|
25 |
2 24
|
syl |
|
26 |
23
|
brrelex2i |
|
27 |
2 26
|
syl |
|
28 |
|
op1stg |
|
29 |
25 27 28
|
syl2anc |
|
30 |
22 29
|
eqtrid |
|
31 |
30
|
adantr |
|
32 |
18 31
|
eqtrd |
|
33 |
|
fvexd |
|
34 |
14
|
adantr |
|
35 |
15
|
adantr |
|
36 |
34 35
|
eqtrd |
|
37 |
36
|
fveq2d |
|
38 |
37
|
fveq2d |
|
39 |
19 20
|
op1st |
|
40 |
39
|
fveq2i |
|
41 |
|
relfunc |
|
42 |
41
|
brrelex1i |
|
43 |
3 42
|
syl |
|
44 |
41
|
brrelex2i |
|
45 |
3 44
|
syl |
|
46 |
|
op1stg |
|
47 |
43 45 46
|
syl2anc |
|
48 |
40 47
|
eqtrid |
|
49 |
48
|
ad2antrr |
|
50 |
38 49
|
eqtrd |
|
51 |
|
fvexd |
|
52 |
34
|
adantr |
|
53 |
35
|
adantr |
|
54 |
52 53
|
eqtrd |
|
55 |
54
|
fveq2d |
|
56 |
55
|
fveq2d |
|
57 |
39
|
fveq2i |
|
58 |
|
op2ndg |
|
59 |
43 45 58
|
syl2anc |
|
60 |
57 59
|
eqtrid |
|
61 |
60
|
ad3antrrr |
|
62 |
56 61
|
eqtrd |
|
63 |
|
fvexd |
|
64 |
|
simp-4r |
|
65 |
64
|
simprd |
|
66 |
7
|
ad4antr |
|
67 |
65 66
|
eqtrd |
|
68 |
67
|
fveq2d |
|
69 |
68
|
fveq2d |
|
70 |
|
opex |
|
71 |
|
opex |
|
72 |
70 71
|
op2nd |
|
73 |
72
|
fveq2i |
|
74 |
23
|
brrelex1i |
|
75 |
5 74
|
syl |
|
76 |
23
|
brrelex2i |
|
77 |
5 76
|
syl |
|
78 |
|
op1stg |
|
79 |
75 77 78
|
syl2anc |
|
80 |
73 79
|
eqtrid |
|
81 |
80
|
ad4antr |
|
82 |
69 81
|
eqtrd |
|
83 |
|
fvexd |
|
84 |
65
|
adantr |
|
85 |
66
|
adantr |
|
86 |
84 85
|
eqtrd |
|
87 |
86
|
fveq2d |
|
88 |
87
|
fveq2d |
|
89 |
70 71
|
op1st |
|
90 |
89
|
fveq2i |
|
91 |
41
|
brrelex1i |
|
92 |
6 91
|
syl |
|
93 |
41
|
brrelex2i |
|
94 |
6 93
|
syl |
|
95 |
|
op1stg |
|
96 |
92 94 95
|
syl2anc |
|
97 |
90 96
|
eqtrid |
|
98 |
97
|
ad5antr |
|
99 |
88 98
|
eqtrd |
|
100 |
55
|
ad3antrrr |
|
101 |
100 39
|
eqtrdi |
|
102 |
87
|
adantr |
|
103 |
102 89
|
eqtrdi |
|
104 |
101 103
|
oveq12d |
|
105 |
17
|
ad5antr |
|
106 |
105 21
|
eqtrdi |
|
107 |
68
|
ad2antrr |
|
108 |
107 72
|
eqtrdi |
|
109 |
106 108
|
oveq12d |
|
110 |
|
simp-4r |
|
111 |
|
simp-5r |
|
112 |
111
|
fveq1d |
|
113 |
110 112
|
fveq12d |
|
114 |
|
simplr |
|
115 |
114
|
fveq1d |
|
116 |
110 115
|
fveq12d |
|
117 |
113 116
|
opeq12d |
|
118 |
|
simpr |
|
119 |
118 115
|
fveq12d |
|
120 |
117 119
|
oveq12d |
|
121 |
115
|
fveq2d |
|
122 |
|
simpllr |
|
123 |
122 112 115
|
oveq123d |
|
124 |
123
|
fveq1d |
|
125 |
120 121 124
|
oveq123d |
|
126 |
125
|
mpteq2dv |
|
127 |
104 109 126
|
mpoeq123dv |
|
128 |
83 99 127
|
csbied2 |
|
129 |
63 82 128
|
csbied2 |
|
130 |
51 62 129
|
csbied2 |
|
131 |
33 50 130
|
csbied2 |
|
132 |
13 32 131
|
csbied2 |
|
133 |
11 4 3 2
|
fuco2eld |
|
134 |
11 7 6 5
|
fuco2eld |
|
135 |
|
ovex |
|
136 |
|
ovex |
|
137 |
135 136
|
mpoex |
|
138 |
137
|
a1i |
|
139 |
12 132 133 134 138
|
ovmpod |
|