Step |
Hyp |
Ref |
Expression |
1 |
|
oveq1 |
|
2 |
1
|
oveq1d |
|
3 |
|
oveq1 |
|
4 |
2 3
|
eqeq12d |
|
5 |
|
oveq2 |
|
6 |
5
|
oveq1d |
|
7 |
|
oveq1 |
|
8 |
7
|
oveq2d |
|
9 |
6 8
|
eqeq12d |
|
10 |
|
oveq2 |
|
11 |
|
oveq2 |
|
12 |
11
|
oveq2d |
|
13 |
10 12
|
eqeq12d |
|
14 |
|
oveq1 |
|
15 |
14
|
oveq1d |
|
16 |
|
oveq1 |
|
17 |
15 16
|
eqeq12d |
|
18 |
|
oveq2 |
|
19 |
18
|
oveq1d |
|
20 |
|
oveq1 |
|
21 |
20
|
oveq2d |
|
22 |
19 21
|
eqeq12d |
|
23 |
5
|
oveq1d |
|
24 |
20
|
oveq2d |
|
25 |
23 24
|
eqeq12d |
|
26 |
|
oveq2 |
|
27 |
11
|
oveq2d |
|
28 |
26 27
|
eqeq12d |
|
29 |
|
oveq1 |
|
30 |
29
|
oveq1d |
|
31 |
|
oveq1 |
|
32 |
30 31
|
eqeq12d |
|
33 |
|
oveq2 |
|
34 |
33
|
oveq1d |
|
35 |
|
oveq1 |
|
36 |
35
|
oveq2d |
|
37 |
34 36
|
eqeq12d |
|
38 |
|
oveq2 |
|
39 |
|
oveq2 |
|
40 |
39
|
oveq2d |
|
41 |
38 40
|
eqeq12d |
|
42 |
|
simpr21 |
|
43 |
|
eleq1 |
|
44 |
43
|
ralimi |
|
45 |
|
ralbi |
|
46 |
42 44 45
|
3syl |
|
47 |
|
simpr23 |
|
48 |
|
eleq1 |
|
49 |
48
|
ralimi |
|
50 |
|
ralbi |
|
51 |
47 49 50
|
3syl |
|
52 |
|
simpr3 |
|
53 |
|
eleq1 |
|
54 |
53
|
ralimi |
|
55 |
|
ralbi |
|
56 |
52 54 55
|
3syl |
|
57 |
46 51 56
|
3anbi123d |
|
58 |
57
|
rabbidv |
|
59 |
58
|
inteqd |
|
60 |
|
naddasslem1 |
|
61 |
60
|
adantr |
|
62 |
|
naddasslem2 |
|
63 |
62
|
adantr |
|
64 |
59 61 63
|
3eqtr4d |
|
65 |
64
|
ex |
|
66 |
4 9 13 17 22 25 28 32 37 41 65
|
on3ind |
|