Step |
Hyp |
Ref |
Expression |
1 |
|
catciso.c |
|
2 |
|
catciso.b |
|
3 |
|
catciso.r |
|
4 |
|
catciso.s |
|
5 |
|
catciso.u |
|
6 |
|
catciso.x |
|
7 |
|
catciso.y |
|
8 |
|
catciso.i |
|
9 |
|
relfunc |
|
10 |
|
eqid |
|
11 |
1
|
catccat |
|
12 |
5 11
|
syl |
|
13 |
2 10 12 6 7 8
|
isoval |
|
14 |
13
|
eleq2d |
|
15 |
14
|
biimpa |
|
16 |
12
|
adantr |
|
17 |
6
|
adantr |
|
18 |
7
|
adantr |
|
19 |
2 10 16 17 18
|
invfun |
|
20 |
|
funfvbrb |
|
21 |
19 20
|
syl |
|
22 |
15 21
|
mpbid |
|
23 |
|
eqid |
|
24 |
2 10 16 17 18 23
|
isinv |
|
25 |
22 24
|
mpbid |
|
26 |
25
|
simpld |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
2 27 28 29 23 16 17 18
|
issect |
|
31 |
26 30
|
mpbid |
|
32 |
31
|
simp1d |
|
33 |
1 2 5 27 6 7
|
catchom |
|
34 |
33
|
adantr |
|
35 |
32 34
|
eleqtrd |
|
36 |
|
1st2nd |
|
37 |
9 35 36
|
sylancr |
|
38 |
|
1st2ndbr |
|
39 |
9 35 38
|
sylancr |
|
40 |
|
eqid |
|
41 |
|
eqid |
|
42 |
39
|
adantr |
|
43 |
|
simprl |
|
44 |
|
simprr |
|
45 |
3 40 41 42 43 44
|
funcf2 |
|
46 |
|
relfunc |
|
47 |
31
|
simp2d |
|
48 |
1 2 5 27 7 6
|
catchom |
|
49 |
48
|
adantr |
|
50 |
47 49
|
eleqtrd |
|
51 |
|
1st2ndbr |
|
52 |
46 50 51
|
sylancr |
|
53 |
52
|
adantr |
|
54 |
3 4 42
|
funcf1 |
|
55 |
54 43
|
ffvelrnd |
|
56 |
54 44
|
ffvelrnd |
|
57 |
4 41 40 53 55 56
|
funcf2 |
|
58 |
31
|
simp3d |
|
59 |
5
|
adantr |
|
60 |
1 2 59 28 17 18 17 35 50
|
catcco |
|
61 |
|
eqid |
|
62 |
1 2 29 61 5 6
|
catcid |
|
63 |
62
|
adantr |
|
64 |
58 60 63
|
3eqtr3d |
|
65 |
64
|
adantr |
|
66 |
65
|
fveq2d |
|
67 |
66
|
fveq1d |
|
68 |
35
|
adantr |
|
69 |
50
|
adantr |
|
70 |
3 68 69 43
|
cofu1 |
|
71 |
1 2 5
|
catcbas |
|
72 |
|
inss2 |
|
73 |
71 72
|
eqsstrdi |
|
74 |
73 6
|
sseldd |
|
75 |
74
|
ad2antrr |
|
76 |
61 3 75 43
|
idfu1 |
|
77 |
67 70 76
|
3eqtr3d |
|
78 |
66
|
fveq1d |
|
79 |
3 68 69 44
|
cofu1 |
|
80 |
61 3 75 44
|
idfu1 |
|
81 |
78 79 80
|
3eqtr3d |
|
82 |
77 81
|
oveq12d |
|
83 |
82
|
feq3d |
|
84 |
57 83
|
mpbid |
|
85 |
65
|
fveq2d |
|
86 |
85
|
oveqd |
|
87 |
3 68 69 43 44
|
cofu2nd |
|
88 |
61 3 75 40 43 44
|
idfu2nd |
|
89 |
86 87 88
|
3eqtr3d |
|
90 |
25
|
simprd |
|
91 |
2 27 28 29 23 16 18 17
|
issect |
|
92 |
90 91
|
mpbid |
|
93 |
92
|
simp3d |
|
94 |
1 2 59 28 18 17 18 50 35
|
catcco |
|
95 |
|
eqid |
|
96 |
1 2 29 95 5 7
|
catcid |
|
97 |
96
|
adantr |
|
98 |
93 94 97
|
3eqtr3d |
|
99 |
98
|
adantr |
|
100 |
99
|
fveq2d |
|
101 |
100
|
oveqd |
|
102 |
4 69 68 55 56
|
cofu2nd |
|
103 |
77 81
|
oveq12d |
|
104 |
103
|
coeq1d |
|
105 |
102 104
|
eqtrd |
|
106 |
73
|
ad2antrr |
|
107 |
7
|
ad2antrr |
|
108 |
106 107
|
sseldd |
|
109 |
95 4 108 41 55 56
|
idfu2nd |
|
110 |
101 105 109
|
3eqtr3d |
|
111 |
45 84 89 110
|
fcof1od |
|
112 |
111
|
ralrimivva |
|
113 |
3 40 41
|
isffth2 |
|
114 |
39 112 113
|
sylanbrc |
|
115 |
|
df-br |
|
116 |
114 115
|
sylib |
|
117 |
37 116
|
eqeltrd |
|
118 |
3 4 39
|
funcf1 |
|
119 |
4 3 52
|
funcf1 |
|
120 |
64
|
fveq2d |
|
121 |
3 35 50
|
cofu1st |
|
122 |
74
|
adantr |
|
123 |
61 3 122
|
idfu1st |
|
124 |
120 121 123
|
3eqtr3d |
|
125 |
98
|
fveq2d |
|
126 |
4 50 35
|
cofu1st |
|
127 |
73 7
|
sseldd |
|
128 |
127
|
adantr |
|
129 |
95 4 128
|
idfu1st |
|
130 |
125 126 129
|
3eqtr3d |
|
131 |
118 119 124 130
|
fcof1od |
|
132 |
117 131
|
jca |
|
133 |
12
|
adantr |
|
134 |
6
|
adantr |
|
135 |
7
|
adantr |
|
136 |
|
inss1 |
|
137 |
|
fullfunc |
|
138 |
136 137
|
sstri |
|
139 |
|
simprl |
|
140 |
138 139
|
sseldi |
|
141 |
9 140 36
|
sylancr |
|
142 |
5
|
adantr |
|
143 |
|
eqid |
|
144 |
141 139
|
eqeltrrd |
|
145 |
144 115
|
sylibr |
|
146 |
|
simprr |
|
147 |
1 2 3 4 142 134 135 10 143 145 146
|
catcisolem |
|
148 |
141 147
|
eqbrtrd |
|
149 |
2 10 133 134 135 8 148
|
inviso1 |
|
150 |
132 149
|
impbida |
|