Step |
Hyp |
Ref |
Expression |
1 |
|
brsegle |
|
2 |
|
simprl |
|
3 |
|
simpl1 |
|
4 |
|
simpl3l |
|
5 |
|
simpl3r |
|
6 |
|
simpr |
|
7 |
|
btwncolinear2 |
|
8 |
3 4 5 6 7
|
syl13anc |
|
9 |
8
|
adantr |
|
10 |
2 9
|
mpd |
|
11 |
|
simpl2l |
|
12 |
|
simpl2r |
|
13 |
|
simprr |
|
14 |
3 11 12 4 6 13
|
cgrcomand |
|
15 |
|
simpl2 |
|
16 |
|
lineext |
|
17 |
3 4 6 5 15 16
|
syl131anc |
|
18 |
17
|
adantr |
|
19 |
10 14 18
|
mp2and |
|
20 |
|
an32 |
|
21 |
|
simpll1 |
|
22 |
|
simpl3l |
|
23 |
22
|
adantr |
|
24 |
|
simpr |
|
25 |
|
simpl3r |
|
26 |
25
|
adantr |
|
27 |
|
simpl2l |
|
28 |
27
|
adantr |
|
29 |
|
simpl2r |
|
30 |
29
|
adantr |
|
31 |
|
simplr |
|
32 |
|
brcgr3 |
|
33 |
21 23 24 26 28 30 31 32
|
syl133anc |
|
34 |
33
|
adantr |
|
35 |
|
simp2l |
|
36 |
|
simp3 |
|
37 |
33
|
3ad2ant1 |
|
38 |
36 37
|
mpbird |
|
39 |
|
btwnxfr |
|
40 |
21 23 24 26 28 30 31 39
|
syl133anc |
|
41 |
40
|
3ad2ant1 |
|
42 |
35 38 41
|
mp2and |
|
43 |
|
simp32 |
|
44 |
|
cgrcom |
|
45 |
21 23 26 28 31 44
|
syl122anc |
|
46 |
45
|
3ad2ant1 |
|
47 |
43 46
|
mpbid |
|
48 |
42 47
|
jca |
|
49 |
48
|
3expia |
|
50 |
34 49
|
sylbid |
|
51 |
20 50
|
sylanb |
|
52 |
51
|
an32s |
|
53 |
52
|
reximdva |
|
54 |
19 53
|
mpd |
|
55 |
54
|
rexlimdva2 |
|
56 |
|
simprl |
|
57 |
|
simpll1 |
|
58 |
27
|
adantr |
|
59 |
|
simplr |
|
60 |
29
|
adantr |
|
61 |
|
btwncolinear1 |
|
62 |
57 58 59 60 61
|
syl13anc |
|
63 |
56 62
|
mpd |
|
64 |
|
simprr |
|
65 |
|
simpl1 |
|
66 |
|
simpr |
|
67 |
|
simpl3 |
|
68 |
|
lineext |
|
69 |
65 27 66 29 67 68
|
syl131anc |
|
70 |
69
|
adantr |
|
71 |
63 64 70
|
mp2and |
|
72 |
27 66 29
|
3jca |
|
73 |
72
|
adantr |
|
74 |
|
brcgr3 |
|
75 |
21 73 23 26 24 74
|
syl113anc |
|
76 |
75
|
adantr |
|
77 |
|
simp2l |
|
78 |
|
simp32 |
|
79 |
|
simp2r |
|
80 |
|
simp33 |
|
81 |
|
cgrcomlr |
|
82 |
21 31 30 26 24 81
|
syl122anc |
|
83 |
82
|
3ad2ant1 |
|
84 |
80 83
|
mpbid |
|
85 |
78 79 84
|
3jca |
|
86 |
|
brcgr3 |
|
87 |
21 28 30 31 23 24 26 86
|
syl133anc |
|
88 |
87
|
3ad2ant1 |
|
89 |
85 88
|
mpbird |
|
90 |
|
btwnxfr |
|
91 |
21 28 30 31 23 24 26 90
|
syl133anc |
|
92 |
91
|
3ad2ant1 |
|
93 |
77 89 92
|
mp2and |
|
94 |
93 78
|
jca |
|
95 |
94
|
3expia |
|
96 |
76 95
|
sylbid |
|
97 |
96
|
an32s |
|
98 |
97
|
reximdva |
|
99 |
71 98
|
mpd |
|
100 |
99
|
rexlimdva2 |
|
101 |
55 100
|
impbid |
|
102 |
1 101
|
bitrd |
|