Step |
Hyp |
Ref |
Expression |
1 |
|
fuciso.q |
|
2 |
|
fuciso.b |
|
3 |
|
fuciso.n |
|
4 |
|
fuciso.f |
|
5 |
|
fuciso.g |
|
6 |
|
fucinv.i |
|
7 |
|
fucinv.j |
|
8 |
|
invfuc.u |
|
9 |
|
invfuc.v |
|
10 |
|
eqid |
|
11 |
|
funcrcl |
|
12 |
4 11
|
syl |
|
13 |
12
|
simprd |
|
14 |
13
|
adantr |
|
15 |
|
relfunc |
|
16 |
|
1st2ndbr |
|
17 |
15 4 16
|
sylancr |
|
18 |
2 10 17
|
funcf1 |
|
19 |
18
|
ffvelrnda |
|
20 |
|
1st2ndbr |
|
21 |
15 5 20
|
sylancr |
|
22 |
2 10 21
|
funcf1 |
|
23 |
22
|
ffvelrnda |
|
24 |
|
eqid |
|
25 |
10 7 14 19 23 24
|
invss |
|
26 |
25
|
ssbrd |
|
27 |
9 26
|
mpd |
|
28 |
|
brxp |
|
29 |
28
|
simprbi |
|
30 |
27 29
|
syl |
|
31 |
30
|
ralrimiva |
|
32 |
2
|
fvexi |
|
33 |
|
mptelixpg |
|
34 |
32 33
|
ax-mp |
|
35 |
31 34
|
sylibr |
|
36 |
|
fveq2 |
|
37 |
|
fveq2 |
|
38 |
36 37
|
oveq12d |
|
39 |
38
|
cbvixpv |
|
40 |
35 39
|
eleqtrdi |
|
41 |
|
simpr2 |
|
42 |
|
simpr |
|
43 |
|
eqid |
|
44 |
43
|
fvmpt2 |
|
45 |
42 30 44
|
syl2anc |
|
46 |
9 45
|
breqtrrd |
|
47 |
46
|
ralrimiva |
|
48 |
47
|
adantr |
|
49 |
|
nfcv |
|
50 |
|
nfcv |
|
51 |
|
nffvmpt1 |
|
52 |
49 50 51
|
nfbr |
|
53 |
|
fveq2 |
|
54 |
|
fveq2 |
|
55 |
|
fveq2 |
|
56 |
54 55
|
oveq12d |
|
57 |
|
fveq2 |
|
58 |
53 56 57
|
breq123d |
|
59 |
52 58
|
rspc |
|
60 |
41 48 59
|
sylc |
|
61 |
13
|
adantr |
|
62 |
18
|
adantr |
|
63 |
62 41
|
ffvelrnd |
|
64 |
22
|
adantr |
|
65 |
64 41
|
ffvelrnd |
|
66 |
|
eqid |
|
67 |
10 7 61 63 65 66
|
isinv |
|
68 |
60 67
|
mpbid |
|
69 |
68
|
simpld |
|
70 |
|
eqid |
|
71 |
|
eqid |
|
72 |
10 24 70 71 66 61 63 65
|
issect |
|
73 |
69 72
|
mpbid |
|
74 |
73
|
simp3d |
|
75 |
74
|
oveq1d |
|
76 |
|
simpr1 |
|
77 |
62 76
|
ffvelrnd |
|
78 |
|
eqid |
|
79 |
17
|
adantr |
|
80 |
2 78 24 79 76 41
|
funcf2 |
|
81 |
|
simpr3 |
|
82 |
80 81
|
ffvelrnd |
|
83 |
10 24 71 61 77 70 63 82
|
catlid |
|
84 |
75 83
|
eqtr2d |
|
85 |
8
|
adantr |
|
86 |
3 85
|
nat1st2nd |
|
87 |
3 86 2 24 41
|
natcl |
|
88 |
73
|
simp2d |
|
89 |
10 24 70 61 77 63 65 82 87 63 88
|
catass |
|
90 |
3 86 2 78 70 76 41 81
|
nati |
|
91 |
90
|
oveq2d |
|
92 |
84 89 91
|
3eqtrd |
|
93 |
92
|
oveq1d |
|
94 |
64 76
|
ffvelrnd |
|
95 |
|
nfcv |
|
96 |
|
nfcv |
|
97 |
|
nffvmpt1 |
|
98 |
95 96 97
|
nfbr |
|
99 |
|
fveq2 |
|
100 |
37 36
|
oveq12d |
|
101 |
|
fveq2 |
|
102 |
99 100 101
|
breq123d |
|
103 |
98 102
|
rspc |
|
104 |
76 48 103
|
sylc |
|
105 |
10 7 61 77 94 66
|
isinv |
|
106 |
104 105
|
mpbid |
|
107 |
106
|
simprd |
|
108 |
10 24 70 71 66 61 94 77
|
issect |
|
109 |
107 108
|
mpbid |
|
110 |
109
|
simp1d |
|
111 |
109
|
simp2d |
|
112 |
21
|
adantr |
|
113 |
2 78 24 112 76 41
|
funcf2 |
|
114 |
113 81
|
ffvelrnd |
|
115 |
10 24 70 61 77 94 65 111 114
|
catcocl |
|
116 |
10 24 70 61 94 77 65 110 115 63 88
|
catass |
|
117 |
3 86 2 24 76
|
natcl |
|
118 |
10 24 70 61 94 77 94 110 117 65 114
|
catass |
|
119 |
109
|
simp3d |
|
120 |
119
|
oveq2d |
|
121 |
10 24 71 61 94 70 65 114
|
catrid |
|
122 |
118 120 121
|
3eqtrd |
|
123 |
122
|
oveq2d |
|
124 |
93 116 123
|
3eqtrrd |
|
125 |
124
|
ralrimivvva |
|
126 |
3 2 78 24 70 5 4
|
isnat2 |
|
127 |
40 125 126
|
mpbir2and |
|
128 |
|
nfv |
|
129 |
128 98 102
|
cbvralw |
|
130 |
47 129
|
sylib |
|
131 |
1 2 3 4 5 6 7
|
fucinv |
|
132 |
8 127 130 131
|
mpbir3and |
|