Step |
Hyp |
Ref |
Expression |
1 |
|
dvval.t |
|
2 |
|
dvval.k |
|
3 |
|
df-dv |
|
4 |
3
|
a1i |
|
5 |
2
|
oveq1i |
|
6 |
|
simprl |
|
7 |
6
|
oveq2d |
|
8 |
7 1
|
eqtr4di |
|
9 |
5 8
|
syl5eqr |
|
10 |
9
|
fveq2d |
|
11 |
|
simprr |
|
12 |
11
|
dmeqd |
|
13 |
|
simpl2 |
|
14 |
13
|
fdmd |
|
15 |
12 14
|
eqtrd |
|
16 |
10 15
|
fveq12d |
|
17 |
15
|
difeq1d |
|
18 |
11
|
fveq1d |
|
19 |
11
|
fveq1d |
|
20 |
18 19
|
oveq12d |
|
21 |
20
|
oveq1d |
|
22 |
17 21
|
mpteq12dv |
|
23 |
22
|
oveq1d |
|
24 |
23
|
xpeq2d |
|
25 |
16 24
|
iuneq12d |
|
26 |
|
simpr |
|
27 |
26
|
oveq2d |
|
28 |
|
simp1 |
|
29 |
|
cnex |
|
30 |
29
|
elpw2 |
|
31 |
28 30
|
sylibr |
|
32 |
29
|
a1i |
|
33 |
|
simp2 |
|
34 |
|
simp3 |
|
35 |
|
elpm2r |
|
36 |
32 31 33 34 35
|
syl22anc |
|
37 |
|
limccl |
|
38 |
|
xpss2 |
|
39 |
37 38
|
ax-mp |
|
40 |
39
|
rgenw |
|
41 |
|
ss2iun |
|
42 |
40 41
|
ax-mp |
|
43 |
|
iunxpconst |
|
44 |
42 43
|
sseqtri |
|
45 |
44
|
a1i |
|
46 |
|
fvex |
|
47 |
46 29
|
xpex |
|
48 |
47
|
ssex |
|
49 |
45 48
|
syl |
|
50 |
4 25 27 31 36 49
|
ovmpodx |
|
51 |
50 45
|
eqsstrd |
|
52 |
50 51
|
jca |
|