Step |
Hyp |
Ref |
Expression |
1 |
|
dprdval.0 |
|
2 |
|
dprdval.w |
|
3 |
|
simpl |
|
4 |
|
reldmdprd |
|
5 |
4
|
brrelex2i |
|
6 |
5
|
adantr |
|
7 |
4
|
brrelex1i |
|
8 |
|
breq1 |
|
9 |
|
oveq1 |
|
10 |
|
fveq2 |
|
11 |
10 1
|
eqtr4di |
|
12 |
11
|
breq2d |
|
13 |
12
|
rabbidv |
|
14 |
|
oveq1 |
|
15 |
13 14
|
mpteq12dv |
|
16 |
15
|
rneqd |
|
17 |
9 16
|
eqeq12d |
|
18 |
8 17
|
imbi12d |
|
19 |
|
df-br |
|
20 |
|
fvex |
|
21 |
20
|
rgenw |
|
22 |
|
ixpexg |
|
23 |
21 22
|
ax-mp |
|
24 |
23
|
mptrabex |
|
25 |
24
|
rnex |
|
26 |
25
|
rgen2w |
|
27 |
|
df-dprd |
|
28 |
27
|
fmpox |
|
29 |
26 28
|
mpbi |
|
30 |
29
|
fdmi |
|
31 |
30
|
eleq2i |
|
32 |
|
opeliunxp |
|
33 |
19 31 32
|
3bitri |
|
34 |
27
|
ovmpt4g |
|
35 |
25 34
|
mp3an3 |
|
36 |
33 35
|
sylbi |
|
37 |
18 36
|
vtoclg |
|
38 |
7 37
|
mpcom |
|
39 |
38
|
sbcth |
|
40 |
6 39
|
syl |
|
41 |
|
simpr |
|
42 |
41
|
breq2d |
|
43 |
41
|
oveq2d |
|
44 |
41
|
dmeqd |
|
45 |
|
simplr |
|
46 |
44 45
|
eqtrd |
|
47 |
46
|
ixpeq1d |
|
48 |
41
|
fveq1d |
|
49 |
48
|
ixpeq2dv |
|
50 |
47 49
|
eqtrd |
|
51 |
50
|
rabeqdv |
|
52 |
51 2
|
eqtr4di |
|
53 |
|
eqidd |
|
54 |
52 53
|
mpteq12dv |
|
55 |
54
|
rneqd |
|
56 |
43 55
|
eqeq12d |
|
57 |
42 56
|
imbi12d |
|
58 |
6 57
|
sbcied |
|
59 |
40 58
|
mpbid |
|
60 |
3 59
|
mpd |
|