Step |
Hyp |
Ref |
Expression |
1 |
|
simpll |
|
2 |
|
simplr |
|
3 |
|
simprr |
|
4 |
1 2 3
|
3jca |
|
5 |
|
simplr1 |
|
6 |
|
simplr3 |
|
7 |
|
df-3an |
|
8 |
|
simp1 |
|
9 |
|
simp3r |
|
10 |
|
simp2l |
|
11 |
|
simp2r |
|
12 |
|
simp3l |
|
13 |
|
simpr2 |
|
14 |
|
simpr3 |
|
15 |
8 9 10 11 12 13 14
|
btwnexchand |
|
16 |
15
|
orcd |
|
17 |
7 16
|
sylan2br |
|
18 |
17
|
expr |
|
19 |
|
simprlr |
|
20 |
|
simprr |
|
21 |
|
btwnconn3 |
|
22 |
8 9 10 12 11 21
|
syl122anc |
|
23 |
22
|
adantr |
|
24 |
19 20 23
|
mp2and |
|
25 |
24
|
expr |
|
26 |
18 25
|
jaod |
|
27 |
26
|
expr |
|
28 |
|
simpll2 |
|
29 |
28
|
adantl |
|
30 |
29
|
necomd |
|
31 |
|
simprlr |
|
32 |
|
simprr |
|
33 |
|
btwnconn1 |
|
34 |
8 9 11 10 12 33
|
syl122anc |
|
35 |
34
|
adantr |
|
36 |
30 31 32 35
|
mp3and |
|
37 |
36
|
expr |
|
38 |
|
df-3an |
|
39 |
|
simpr3 |
|
40 |
|
simpr2 |
|
41 |
8 9 12 11 10 39 40
|
btwnexchand |
|
42 |
41
|
olcd |
|
43 |
38 42
|
sylan2br |
|
44 |
43
|
expr |
|
45 |
37 44
|
jaod |
|
46 |
45
|
expr |
|
47 |
27 46
|
jaod |
|
48 |
47
|
imp32 |
|
49 |
5 6 48
|
3jca |
|
50 |
49
|
exp31 |
|
51 |
4 50
|
syl5 |
|
52 |
51
|
impd |
|
53 |
|
broutsideof2 |
|
54 |
8 9 10 11 53
|
syl13anc |
|
55 |
|
broutsideof2 |
|
56 |
8 9 11 12 55
|
syl13anc |
|
57 |
54 56
|
anbi12d |
|
58 |
|
df-3an |
|
59 |
|
df-3an |
|
60 |
58 59
|
anbi12i |
|
61 |
|
an4 |
|
62 |
60 61
|
bitr4i |
|
63 |
57 62
|
bitrdi |
|
64 |
|
broutsideof2 |
|
65 |
8 9 10 12 64
|
syl13anc |
|
66 |
52 63 65
|
3imtr4d |
|