Step |
Hyp |
Ref |
Expression |
1 |
|
broutsideof2 |
|
2 |
|
simpl |
|
3 |
|
simpr3 |
|
4 |
|
simpr1 |
|
5 |
|
btwndiff |
|
6 |
2 3 4 5
|
syl3anc |
|
7 |
6
|
adantr |
|
8 |
|
df-3an |
|
9 |
|
3anass |
|
10 |
|
simpr3 |
|
11 |
10
|
necomd |
|
12 |
|
simp1 |
|
13 |
|
simp23 |
|
14 |
|
simp22 |
|
15 |
|
simp21 |
|
16 |
|
simp3 |
|
17 |
|
simpr1r |
|
18 |
12 14 15 13 17
|
btwncomand |
|
19 |
|
simpr2 |
|
20 |
12 13 14 15 16 18 19
|
btwnexch3and |
|
21 |
11 20 19
|
3jca |
|
22 |
8 9 21
|
syl2anbr |
|
23 |
22
|
expr |
|
24 |
23
|
an32s |
|
25 |
24
|
reximdva |
|
26 |
7 25
|
mpd |
|
27 |
26
|
expr |
|
28 |
|
simpr2 |
|
29 |
|
btwndiff |
|
30 |
2 28 4 29
|
syl3anc |
|
31 |
30
|
adantr |
|
32 |
|
3anass |
|
33 |
|
simpr3 |
|
34 |
33
|
necomd |
|
35 |
|
simpr2 |
|
36 |
|
simpr1r |
|
37 |
12 13 15 14 36
|
btwncomand |
|
38 |
12 14 13 15 16 37 35
|
btwnexch3and |
|
39 |
34 35 38
|
3jca |
|
40 |
8 32 39
|
syl2anbr |
|
41 |
40
|
expr |
|
42 |
41
|
an32s |
|
43 |
42
|
reximdva |
|
44 |
31 43
|
mpd |
|
45 |
44
|
expr |
|
46 |
27 45
|
jaod |
|
47 |
|
simprr1 |
|
48 |
|
simpll |
|
49 |
|
simplr1 |
|
50 |
|
simplr2 |
|
51 |
|
simpr |
|
52 |
|
simprr2 |
|
53 |
48 49 50 51 52
|
btwncomand |
|
54 |
|
simplr3 |
|
55 |
|
simprr3 |
|
56 |
48 49 54 51 55
|
btwncomand |
|
57 |
|
btwnconn2 |
|
58 |
48 51 49 50 54 57
|
syl122anc |
|
59 |
58
|
adantr |
|
60 |
47 53 56 59
|
mp3and |
|
61 |
60
|
expr |
|
62 |
61
|
an32s |
|
63 |
62
|
rexlimdva |
|
64 |
46 63
|
impbid |
|
65 |
64
|
pm5.32da |
|
66 |
|
df-3an |
|
67 |
|
df-3an |
|
68 |
65 66 67
|
3bitr4g |
|
69 |
1 68
|
bitrd |
|