Step |
Hyp |
Ref |
Expression |
1 |
|
prfval.k |
|
2 |
|
prfval.b |
|
3 |
|
prfval.h |
|
4 |
|
prfval.c |
|
5 |
|
prfval.d |
|
6 |
|
df-prf |
|
7 |
6
|
a1i |
|
8 |
|
fvex |
|
9 |
8
|
dmex |
|
10 |
9
|
a1i |
|
11 |
|
simprl |
|
12 |
11
|
fveq2d |
|
13 |
12
|
dmeqd |
|
14 |
|
eqid |
|
15 |
|
relfunc |
|
16 |
|
1st2ndbr |
|
17 |
15 4 16
|
sylancr |
|
18 |
2 14 17
|
funcf1 |
|
19 |
18
|
fdmd |
|
20 |
19
|
adantr |
|
21 |
13 20
|
eqtrd |
|
22 |
|
simpr |
|
23 |
|
simplrl |
|
24 |
23
|
fveq2d |
|
25 |
24
|
fveq1d |
|
26 |
|
simplrr |
|
27 |
26
|
fveq2d |
|
28 |
27
|
fveq1d |
|
29 |
25 28
|
opeq12d |
|
30 |
22 29
|
mpteq12dv |
|
31 |
|
eqidd |
|
32 |
22 22 31
|
mpoeq123dv |
|
33 |
23
|
ad2antrr |
|
34 |
33
|
fveq2d |
|
35 |
34
|
oveqd |
|
36 |
35
|
dmeqd |
|
37 |
|
eqid |
|
38 |
17
|
ad4antr |
|
39 |
|
simplr |
|
40 |
|
simpr |
|
41 |
2 3 37 38 39 40
|
funcf2 |
|
42 |
41
|
fdmd |
|
43 |
36 42
|
eqtrd |
|
44 |
35
|
fveq1d |
|
45 |
26
|
ad2antrr |
|
46 |
45
|
fveq2d |
|
47 |
46
|
oveqd |
|
48 |
47
|
fveq1d |
|
49 |
44 48
|
opeq12d |
|
50 |
43 49
|
mpteq12dv |
|
51 |
50
|
3impa |
|
52 |
51
|
mpoeq3dva |
|
53 |
32 52
|
eqtrd |
|
54 |
30 53
|
opeq12d |
|
55 |
10 21 54
|
csbied2 |
|
56 |
4
|
elexd |
|
57 |
5
|
elexd |
|
58 |
|
opex |
|
59 |
58
|
a1i |
|
60 |
7 55 56 57 59
|
ovmpod |
|
61 |
1 60
|
syl5eq |
|