Step |
Hyp |
Ref |
Expression |
1 |
|
simprll |
|
2 |
|
simprrr |
|
3 |
1 2
|
jca |
|
4 |
|
simpl1 |
|
5 |
|
simpl23 |
|
6 |
|
simprl |
|
7 |
|
simpl31 |
|
8 |
|
simpl32 |
|
9 |
|
simprr |
|
10 |
|
cgrxfr |
|
11 |
4 5 6 7 8 9 10
|
syl132anc |
|
12 |
11
|
adantr |
|
13 |
3 12
|
mpd |
|
14 |
|
anass |
|
15 |
|
df-3an |
|
16 |
15
|
anbi2i |
|
17 |
14 16
|
bitr4i |
|
18 |
|
simpl1 |
|
19 |
|
simpl23 |
|
20 |
|
simpr1 |
|
21 |
|
simpl31 |
|
22 |
|
simpl32 |
|
23 |
|
simpr3 |
|
24 |
|
simpr2 |
|
25 |
|
brcgr3 |
|
26 |
18 19 20 21 22 23 24 25
|
syl133anc |
|
27 |
26
|
anbi2d |
|
28 |
27
|
adantr |
|
29 |
|
df-3an |
|
30 |
|
simpl33 |
|
31 |
|
simpr3l |
|
32 |
|
simpr2l |
|
33 |
18 22 23 24 30 31 32
|
btwnexchand |
|
34 |
|
simpl21 |
|
35 |
|
simpl22 |
|
36 |
|
simpr1r |
|
37 |
|
simp3r1 |
|
38 |
37
|
adantl |
|
39 |
18 34 35 19 20 22 23 36 38
|
cgrtrand |
|
40 |
33 39
|
jca |
|
41 |
29 40
|
sylan2br |
|
42 |
41
|
expr |
|
43 |
28 42
|
sylbid |
|
44 |
17 43
|
sylanb |
|
45 |
44
|
an32s |
|
46 |
45
|
reximdva |
|
47 |
13 46
|
mpd |
|
48 |
47
|
exp31 |
|
49 |
48
|
rexlimdvv |
|
50 |
|
simp1 |
|
51 |
|
simp21 |
|
52 |
|
simp22 |
|
53 |
|
simp23 |
|
54 |
|
simp31 |
|
55 |
|
brsegle |
|
56 |
50 51 52 53 54 55
|
syl122anc |
|
57 |
|
simp32 |
|
58 |
|
simp33 |
|
59 |
|
brsegle |
|
60 |
50 53 54 57 58 59
|
syl122anc |
|
61 |
56 60
|
anbi12d |
|
62 |
|
reeanv |
|
63 |
61 62
|
bitr4di |
|
64 |
|
brsegle |
|
65 |
50 51 52 57 58 64
|
syl122anc |
|
66 |
49 63 65
|
3imtr4d |
|