Step |
Hyp |
Ref |
Expression |
1 |
|
ofpreima.1 |
|
2 |
|
ofpreima.2 |
|
3 |
|
ofpreima.3 |
|
4 |
|
ofpreima.4 |
|
5 |
|
nfmpt1 |
|
6 |
|
eqidd |
|
7 |
|
fnov |
|
8 |
4 7
|
sylib |
|
9 |
5 1 2 3 6 8
|
ofoprabco |
|
10 |
9
|
cnveqd |
|
11 |
|
cnvco |
|
12 |
10 11
|
eqtrdi |
|
13 |
12
|
imaeq1d |
|
14 |
|
imaco |
|
15 |
13 14
|
eqtrdi |
|
16 |
|
dfima2 |
|
17 |
|
vex |
|
18 |
|
vex |
|
19 |
17 18
|
brcnv |
|
20 |
|
funmpt |
|
21 |
|
funbrfv2b |
|
22 |
20 21
|
ax-mp |
|
23 |
|
opex |
|
24 |
|
eqid |
|
25 |
23 24
|
dmmpti |
|
26 |
25
|
eleq2i |
|
27 |
26
|
anbi1i |
|
28 |
22 27
|
bitri |
|
29 |
|
fveq2 |
|
30 |
|
fveq2 |
|
31 |
29 30
|
opeq12d |
|
32 |
|
opex |
|
33 |
31 24 32
|
fvmpt |
|
34 |
33
|
eqeq1d |
|
35 |
34
|
pm5.32i |
|
36 |
19 28 35
|
3bitri |
|
37 |
36
|
rexbii |
|
38 |
37
|
abbii |
|
39 |
|
nfv |
|
40 |
|
nfab1 |
|
41 |
|
nfcv |
|
42 |
|
eliun |
|
43 |
|
ffn |
|
44 |
|
fniniseg |
|
45 |
1 43 44
|
3syl |
|
46 |
|
ffn |
|
47 |
|
fniniseg |
|
48 |
2 46 47
|
3syl |
|
49 |
45 48
|
anbi12d |
|
50 |
|
elin |
|
51 |
|
anandi |
|
52 |
49 50 51
|
3bitr4g |
|
53 |
52
|
adantr |
|
54 |
|
cnvimass |
|
55 |
4
|
fndmd |
|
56 |
54 55
|
sseqtrid |
|
57 |
56
|
sselda |
|
58 |
|
1st2nd2 |
|
59 |
|
eqeq2 |
|
60 |
57 58 59
|
3syl |
|
61 |
|
fvex |
|
62 |
|
fvex |
|
63 |
61 62
|
opth |
|
64 |
60 63
|
syl6bb |
|
65 |
64
|
anbi2d |
|
66 |
53 65
|
bitr4d |
|
67 |
66
|
rexbidva |
|
68 |
|
abid |
|
69 |
67 68
|
bitr4di |
|
70 |
42 69
|
syl5rbb |
|
71 |
39 40 41 70
|
eqrd |
|
72 |
38 71
|
syl5eq |
|
73 |
16 72
|
syl5eq |
|
74 |
15 73
|
eqtrd |
|