Step |
Hyp |
Ref |
Expression |
1 |
|
oddz |
|
2 |
|
evenz |
|
3 |
|
zaddcl |
|
4 |
1 2 3
|
syl2an |
|
5 |
|
eqeq1 |
|
6 |
5
|
rexbidv |
|
7 |
|
dfodd6 |
|
8 |
6 7
|
elrab2 |
|
9 |
|
eqeq1 |
|
10 |
9
|
rexbidv |
|
11 |
|
dfeven4 |
|
12 |
10 11
|
elrab2 |
|
13 |
|
zaddcl |
|
14 |
13
|
ex |
|
15 |
14
|
ad3antlr |
|
16 |
15
|
imp |
|
17 |
16
|
adantr |
|
18 |
|
oveq2 |
|
19 |
18
|
oveq1d |
|
20 |
19
|
eqeq2d |
|
21 |
20
|
adantl |
|
22 |
|
oveq12 |
|
23 |
22
|
ex |
|
24 |
23
|
ad3antlr |
|
25 |
24
|
imp |
|
26 |
|
2cnd |
|
27 |
|
zcn |
|
28 |
27
|
adantl |
|
29 |
26 28
|
mulcld |
|
30 |
29
|
ancoms |
|
31 |
|
1cnd |
|
32 |
|
2cnd |
|
33 |
|
zcn |
|
34 |
|
mulcl |
|
35 |
32 33 34
|
syl2an |
|
36 |
30 31 35
|
add32d |
|
37 |
|
2cnd |
|
38 |
27
|
adantr |
|
39 |
33
|
adantl |
|
40 |
37 38 39
|
adddid |
|
41 |
40
|
eqcomd |
|
42 |
41
|
oveq1d |
|
43 |
36 42
|
eqtrd |
|
44 |
43
|
ex |
|
45 |
44
|
ad3antlr |
|
46 |
45
|
imp |
|
47 |
46
|
adantr |
|
48 |
25 47
|
eqtrd |
|
49 |
17 21 48
|
rspcedvd |
|
50 |
49
|
rexlimdva2 |
|
51 |
50
|
expimpd |
|
52 |
51
|
r19.29an |
|
53 |
12 52
|
syl5bi |
|
54 |
8 53
|
sylbi |
|
55 |
54
|
imp |
|
56 |
|
eqeq1 |
|
57 |
56
|
rexbidv |
|
58 |
|
dfodd6 |
|
59 |
57 58
|
elrab2 |
|
60 |
4 55 59
|
sylanbrc |
|