Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
fveq2 |
|
3 |
2
|
eleq2d |
|
4 |
2
|
eleq2d |
|
5 |
3 4
|
3anbi12d |
|
6 |
5
|
anbi1d |
|
7 |
6
|
rspcev |
|
8 |
1 7
|
mpanr2 |
|
9 |
|
simpr1 |
|
10 |
|
simpr2 |
|
11 |
|
colinearex |
|
12 |
11
|
cnvex |
|
13 |
|
ecexg |
|
14 |
12 13
|
ax-mp |
|
15 |
|
eleq1 |
|
16 |
|
neeq1 |
|
17 |
15 16
|
3anbi13d |
|
18 |
|
opeq1 |
|
19 |
18
|
eceq1d |
|
20 |
19
|
eqeq2d |
|
21 |
17 20
|
anbi12d |
|
22 |
21
|
rexbidv |
|
23 |
|
eleq1 |
|
24 |
|
neeq2 |
|
25 |
23 24
|
3anbi23d |
|
26 |
|
opeq2 |
|
27 |
26
|
eceq1d |
|
28 |
27
|
eqeq2d |
|
29 |
25 28
|
anbi12d |
|
30 |
29
|
rexbidv |
|
31 |
|
eqeq1 |
|
32 |
31
|
anbi2d |
|
33 |
32
|
rexbidv |
|
34 |
22 30 33
|
eloprabg |
|
35 |
14 34
|
mp3an3 |
|
36 |
9 10 35
|
syl2anc |
|
37 |
8 36
|
mpbird |
|
38 |
|
df-ov |
|
39 |
|
df-br |
|
40 |
|
df-line2 |
|
41 |
40
|
eleq2i |
|
42 |
39 41
|
bitri |
|
43 |
|
funline |
|
44 |
|
funbrfv |
|
45 |
43 44
|
ax-mp |
|
46 |
42 45
|
sylbir |
|
47 |
38 46
|
syl5eq |
|
48 |
37 47
|
syl |
|
49 |
|
opex |
|
50 |
|
dfec2 |
|
51 |
49 50
|
ax-mp |
|
52 |
|
vex |
|
53 |
49 52
|
brcnv |
|
54 |
53
|
abbii |
|
55 |
51 54
|
eqtri |
|
56 |
48 55
|
eqtrdi |
|