Step |
Hyp |
Ref |
Expression |
1 |
|
cyccom.c |
|
2 |
|
cyccom.d |
|
3 |
|
cyccom.x |
|
4 |
|
cyccom.y |
|
5 |
|
cyccom.z |
|
6 |
|
eqeq1 |
|
7 |
6
|
rexbidv |
|
8 |
7
|
rspccv |
|
9 |
1 8
|
syl |
|
10 |
|
eqeq1 |
|
11 |
10
|
rexbidv |
|
12 |
11
|
rspccv |
|
13 |
1 12
|
syl |
|
14 |
|
oveq1 |
|
15 |
14
|
eqeq2d |
|
16 |
15
|
cbvrexvw |
|
17 |
|
reeanv |
|
18 |
5
|
sseld |
|
19 |
18
|
com12 |
|
20 |
19
|
adantr |
|
21 |
20
|
impcom |
|
22 |
5
|
sseld |
|
23 |
22
|
a1d |
|
24 |
23
|
imp32 |
|
25 |
21 24
|
addcomd |
|
26 |
25
|
oveq1d |
|
27 |
|
simpr |
|
28 |
2
|
adantr |
|
29 |
|
oveq1 |
|
30 |
29
|
oveq1d |
|
31 |
|
oveq1 |
|
32 |
31
|
oveq1d |
|
33 |
30 32
|
eqeq12d |
|
34 |
|
oveq2 |
|
35 |
34
|
oveq1d |
|
36 |
|
oveq1 |
|
37 |
36
|
oveq2d |
|
38 |
35 37
|
eqeq12d |
|
39 |
33 38
|
rspc2va |
|
40 |
27 28 39
|
syl2anc |
|
41 |
27
|
ancomd |
|
42 |
|
oveq1 |
|
43 |
42
|
oveq1d |
|
44 |
|
oveq1 |
|
45 |
44
|
oveq1d |
|
46 |
43 45
|
eqeq12d |
|
47 |
|
oveq2 |
|
48 |
47
|
oveq1d |
|
49 |
|
oveq1 |
|
50 |
49
|
oveq2d |
|
51 |
48 50
|
eqeq12d |
|
52 |
46 51
|
rspc2va |
|
53 |
41 28 52
|
syl2anc |
|
54 |
26 40 53
|
3eqtr3d |
|
55 |
|
oveq12 |
|
56 |
|
oveq12 |
|
57 |
56
|
ancoms |
|
58 |
55 57
|
eqeq12d |
|
59 |
54 58
|
syl5ibrcom |
|
60 |
59
|
rexlimdvva |
|
61 |
17 60
|
syl5bir |
|
62 |
61
|
expd |
|
63 |
16 62
|
syl7bi |
|
64 |
13 63
|
syld |
|
65 |
64
|
com23 |
|
66 |
9 65
|
syld |
|
67 |
4 3 66
|
mp2d |
|