Step |
Hyp |
Ref |
Expression |
1 |
|
isperp.p |
|
2 |
|
isperp.d |
|
3 |
|
isperp.i |
|
4 |
|
isperp.l |
|
5 |
|
isperp.g |
|
6 |
|
isperp.a |
|
7 |
|
foot.x |
|
8 |
|
foot.y |
|
9 |
1 2 3 4 5 6 7 8
|
footex |
|
10 |
|
eqid |
|
11 |
5
|
ad2antrr |
|
12 |
7
|
ad2antrr |
|
13 |
5
|
adantr |
|
14 |
6
|
adantr |
|
15 |
|
simprl |
|
16 |
1 4 3 13 14 15
|
tglnpt |
|
17 |
16
|
adantr |
|
18 |
|
simprr |
|
19 |
1 4 3 13 14 18
|
tglnpt |
|
20 |
19
|
adantr |
|
21 |
8
|
adantr |
|
22 |
|
nelne2 |
|
23 |
15 21 22
|
syl2anc |
|
24 |
23
|
necomd |
|
25 |
24
|
adantr |
|
26 |
1 3 4 11 12 17 25
|
tglinerflx1 |
|
27 |
18
|
adantr |
|
28 |
|
simprl |
|
29 |
7
|
adantr |
|
30 |
1 3 4 13 29 16 24
|
tgelrnln |
|
31 |
1 3 4 13 29 16 24
|
tglinerflx2 |
|
32 |
31 15
|
elind |
|
33 |
1 2 3 4 13 30 14 32
|
isperp2 |
|
34 |
33
|
adantr |
|
35 |
28 34
|
mpbid |
|
36 |
|
id |
|
37 |
|
eqidd |
|
38 |
|
eqidd |
|
39 |
36 37 38
|
s3eqd |
|
40 |
39
|
eleq1d |
|
41 |
|
eqidd |
|
42 |
|
eqidd |
|
43 |
|
id |
|
44 |
41 42 43
|
s3eqd |
|
45 |
44
|
eleq1d |
|
46 |
40 45
|
rspc2va |
|
47 |
26 27 35 46
|
syl21anc |
|
48 |
|
nelne2 |
|
49 |
18 21 48
|
syl2anc |
|
50 |
49
|
necomd |
|
51 |
50
|
adantr |
|
52 |
1 3 4 11 12 20 51
|
tglinerflx1 |
|
53 |
15
|
adantr |
|
54 |
|
simprr |
|
55 |
1 3 4 13 29 19 50
|
tgelrnln |
|
56 |
1 3 4 13 29 19 50
|
tglinerflx2 |
|
57 |
56 18
|
elind |
|
58 |
1 2 3 4 13 55 14 57
|
isperp2 |
|
59 |
58
|
adantr |
|
60 |
54 59
|
mpbid |
|
61 |
|
eqidd |
|
62 |
36 61 38
|
s3eqd |
|
63 |
62
|
eleq1d |
|
64 |
|
eqidd |
|
65 |
|
eqidd |
|
66 |
|
id |
|
67 |
64 65 66
|
s3eqd |
|
68 |
67
|
eleq1d |
|
69 |
63 68
|
rspc2va |
|
70 |
52 53 60 69
|
syl21anc |
|
71 |
1 2 3 4 10 11 12 17 20 47 70
|
ragflat |
|
72 |
71
|
ex |
|
73 |
72
|
ralrimivva |
|
74 |
|
oveq2 |
|
75 |
74
|
breq1d |
|
76 |
75
|
rmo4 |
|
77 |
73 76
|
sylibr |
|
78 |
|
reu5 |
|
79 |
9 77 78
|
sylanbrc |
|