Step |
Hyp |
Ref |
Expression |
1 |
|
tgbtwnconn1.p |
|
2 |
|
tgbtwnconn1.i |
|
3 |
|
tgbtwnconn1.g |
|
4 |
|
tgbtwnconn1.a |
|
5 |
|
tgbtwnconn1.b |
|
6 |
|
tgbtwnconn1.c |
|
7 |
|
tgbtwnconn1.d |
|
8 |
|
tgbtwnconn1.1 |
|
9 |
|
tgbtwnconn1.2 |
|
10 |
|
tgbtwnconn1.3 |
|
11 |
|
simpllr |
|
12 |
11
|
simpld |
|
13 |
12
|
adantr |
|
14 |
|
simpr |
|
15 |
14
|
oveq2d |
|
16 |
13 15
|
eleqtrrd |
|
17 |
16
|
olcd |
|
18 |
|
simprl |
|
19 |
18
|
adantr |
|
20 |
|
simpr |
|
21 |
20
|
oveq2d |
|
22 |
19 21
|
eleqtrrd |
|
23 |
22
|
orcd |
|
24 |
|
df-ne |
|
25 |
3
|
ad4antr |
|
26 |
25
|
ad7antr |
|
27 |
4
|
ad4antr |
|
28 |
27
|
ad7antr |
|
29 |
5
|
ad4antr |
|
30 |
29
|
ad7antr |
|
31 |
6
|
ad4antr |
|
32 |
31
|
ad7antr |
|
33 |
7
|
ad4antr |
|
34 |
33
|
ad7antr |
|
35 |
|
simp-11l |
|
36 |
35 8
|
syl |
|
37 |
35 9
|
syl |
|
38 |
35 10
|
syl |
|
39 |
|
eqid |
|
40 |
|
simp-4r |
|
41 |
40
|
ad7antr |
|
42 |
|
simplr |
|
43 |
42
|
ad7antr |
|
44 |
|
simp-6r |
|
45 |
|
simp-4r |
|
46 |
12
|
ad7antr |
|
47 |
18
|
ad7antr |
|
48 |
|
simp-5r |
|
49 |
48
|
simpld |
|
50 |
|
simpllr |
|
51 |
50
|
simpld |
|
52 |
11
|
simprd |
|
53 |
52
|
ad7antr |
|
54 |
1 39 2 26 34 41 34 32 53
|
tgcgrcomlr |
|
55 |
|
simprr |
|
56 |
55
|
ad7antr |
|
57 |
48
|
simprd |
|
58 |
50
|
simprd |
|
59 |
|
simplr |
|
60 |
|
simprl |
|
61 |
|
simprr |
|
62 |
|
simp-7r |
|
63 |
1 2 26 28 30 32 34 36 37 38 39 41 43 44 45 46 47 49 51 54 56 57 58 59 60 61 62
|
tgbtwnconn1lem3 |
|
64 |
1 39 2 25 27 31 42 18
|
tgbtwncom |
|
65 |
1 39 2 25 27 33 40 12
|
tgbtwncom |
|
66 |
1 39 2 25 42 40 27 31 33 64 65
|
axtgpasch |
|
67 |
66
|
ad5antr |
|
68 |
63 67
|
r19.29a |
|
69 |
1 39 2 25 27 42 29 33
|
axtgsegcon |
|
70 |
69
|
ad3antrrr |
|
71 |
68 70
|
r19.29a |
|
72 |
1 39 2 25 27 40 29 31
|
axtgsegcon |
|
73 |
72
|
adantr |
|
74 |
71 73
|
r19.29a |
|
75 |
74
|
ex |
|
76 |
24 75
|
syl5bir |
|
77 |
76
|
orrd |
|
78 |
17 23 77
|
mpjaodan |
|
79 |
1 39 2 3 4 6 6 7
|
axtgsegcon |
|
80 |
79
|
ad2antrr |
|
81 |
78 80
|
r19.29a |
|
82 |
1 39 2 3 4 7 7 6
|
axtgsegcon |
|
83 |
81 82
|
r19.29a |
|