Step |
Hyp |
Ref |
Expression |
1 |
|
df-3an |
|
2 |
|
simpr11 |
|
3 |
|
simpr12 |
|
4 |
|
simpr13 |
|
5 |
|
simp1 |
|
6 |
|
simp3r |
|
7 |
|
simp2l |
|
8 |
|
simp3l |
|
9 |
|
simpr2 |
|
10 |
5 6 7 8 9
|
btwncomand |
|
11 |
|
simp2r |
|
12 |
|
simpr3 |
|
13 |
5 6 11 8 12
|
btwncomand |
|
14 |
|
btwnconn2 |
|
15 |
14
|
3com23 |
|
16 |
15
|
adantr |
|
17 |
4 10 13 16
|
mp3and |
|
18 |
2 3 17
|
3jca |
|
19 |
1 18
|
sylan2br |
|
20 |
19
|
expr |
|
21 |
|
simp3 |
|
22 |
|
df-3an |
|
23 |
|
simpr11 |
|
24 |
|
simpr3 |
|
25 |
5 7 6 11 24
|
btwncomand |
|
26 |
|
simpr2 |
|
27 |
|
btwnouttr2 |
|
28 |
5 11 7 6 8 27
|
syl122anc |
|
29 |
28
|
adantr |
|
30 |
23 25 26 29
|
mp3and |
|
31 |
22 30
|
sylan2br |
|
32 |
31
|
expr |
|
33 |
|
df-3an |
|
34 |
|
simpr3 |
|
35 |
5 11 6 7 34
|
btwncomand |
|
36 |
|
simpr2 |
|
37 |
5 7 11 6 8 35 36
|
btwnexch3and |
|
38 |
33 37
|
sylan2br |
|
39 |
38
|
expr |
|
40 |
32 39
|
jaod |
|
41 |
21 40
|
syl5 |
|
42 |
20 41
|
impbid |
|
43 |
|
broutsideof2 |
|
44 |
5 6 7 11 43
|
syl13anc |
|
45 |
44
|
adantr |
|
46 |
42 45
|
bitr4d |
|
47 |
46
|
ex |
|