Step |
Hyp |
Ref |
Expression |
1 |
|
fiun.1 |
|
2 |
|
fiun.2 |
|
3 |
|
vex |
|
4 |
|
eqeq1 |
|
5 |
4
|
rexbidv |
|
6 |
3 5
|
elab |
|
7 |
|
r19.29 |
|
8 |
|
nfv |
|
9 |
|
nfre1 |
|
10 |
9
|
nfab |
|
11 |
|
nfv |
|
12 |
10 11
|
nfralw |
|
13 |
8 12
|
nfan |
|
14 |
|
ffun |
|
15 |
|
funeq |
|
16 |
|
bianir |
|
17 |
14 15 16
|
syl2an |
|
18 |
17
|
adantlr |
|
19 |
1
|
fiunlem |
|
20 |
18 19
|
jca |
|
21 |
20
|
a1i |
|
22 |
13 21
|
rexlimi |
|
23 |
7 22
|
syl |
|
24 |
6 23
|
sylan2b |
|
25 |
24
|
ralrimiva |
|
26 |
|
fununi |
|
27 |
25 26
|
syl |
|
28 |
2
|
dfiun2 |
|
29 |
28
|
funeqi |
|
30 |
27 29
|
sylibr |
|
31 |
3
|
eldm2 |
|
32 |
|
fdm |
|
33 |
32
|
eleq2d |
|
34 |
31 33
|
bitr3id |
|
35 |
34
|
adantr |
|
36 |
35
|
ralrexbid |
|
37 |
|
eliun |
|
38 |
37
|
exbii |
|
39 |
3
|
eldm2 |
|
40 |
|
rexcom4 |
|
41 |
38 39 40
|
3bitr4i |
|
42 |
|
eliun |
|
43 |
36 41 42
|
3bitr4g |
|
44 |
43
|
eqrdv |
|
45 |
|
df-fn |
|
46 |
30 44 45
|
sylanbrc |
|
47 |
|
rniun |
|
48 |
|
frn |
|
49 |
48
|
adantr |
|
50 |
49
|
ralimi |
|
51 |
|
iunss |
|
52 |
50 51
|
sylibr |
|
53 |
47 52
|
eqsstrid |
|
54 |
|
df-f |
|
55 |
46 53 54
|
sylanbrc |
|