Step |
Hyp |
Ref |
Expression |
1 |
|
df-colinear |
|
2 |
1
|
breqi |
|
3 |
|
simpr1 |
|
4 |
|
opex |
|
5 |
|
brcnvg |
|
6 |
3 4 5
|
sylancl |
|
7 |
|
df-br |
|
8 |
|
eleq1 |
|
9 |
8
|
3anbi2d |
|
10 |
|
opeq1 |
|
11 |
10
|
breq2d |
|
12 |
|
breq1 |
|
13 |
|
opeq2 |
|
14 |
13
|
breq2d |
|
15 |
11 12 14
|
3orbi123d |
|
16 |
9 15
|
anbi12d |
|
17 |
16
|
rexbidv |
|
18 |
|
eleq1 |
|
19 |
18
|
3anbi3d |
|
20 |
|
opeq2 |
|
21 |
20
|
breq2d |
|
22 |
|
opeq1 |
|
23 |
22
|
breq2d |
|
24 |
|
breq1 |
|
25 |
21 23 24
|
3orbi123d |
|
26 |
19 25
|
anbi12d |
|
27 |
26
|
rexbidv |
|
28 |
|
eleq1 |
|
29 |
28
|
3anbi1d |
|
30 |
|
breq1 |
|
31 |
|
opeq2 |
|
32 |
31
|
breq2d |
|
33 |
|
opeq1 |
|
34 |
33
|
breq2d |
|
35 |
30 32 34
|
3orbi123d |
|
36 |
29 35
|
anbi12d |
|
37 |
36
|
rexbidv |
|
38 |
17 27 37
|
eloprabg |
|
39 |
38
|
3comr |
|
40 |
39
|
adantl |
|
41 |
|
simpl |
|
42 |
|
simp2 |
|
43 |
42
|
anim2i |
|
44 |
|
3simpa |
|
45 |
44
|
anim2i |
|
46 |
|
axdimuniq |
|
47 |
46
|
adantrrl |
|
48 |
|
simprrl |
|
49 |
|
fveq2 |
|
50 |
49
|
eleq2d |
|
51 |
48 50
|
syl5ibrcom |
|
52 |
47 51
|
mpd |
|
53 |
43 45 52
|
syl2an |
|
54 |
53
|
exp32 |
|
55 |
41 54
|
syl7 |
|
56 |
55
|
rexlimdv |
|
57 |
40 56
|
sylbid |
|
58 |
7 57
|
syl5bi |
|
59 |
6 58
|
sylbid |
|
60 |
2 59
|
syl5bi |
|