Step |
Hyp |
Ref |
Expression |
1 |
|
simp1 |
|
2 |
|
simp2l |
|
3 |
|
simp3r |
|
4 |
|
simp3 |
|
5 |
|
axsegcon |
|
6 |
1 2 3 4 5
|
syl121anc |
|
7 |
|
simp3l |
|
8 |
|
axsegcon |
|
9 |
1 2 7 4 8
|
syl121anc |
|
10 |
|
reeanv |
|
11 |
6 9 10
|
sylanbrc |
|
12 |
11
|
adantr |
|
13 |
|
simpl1 |
|
14 |
|
simpl2l |
|
15 |
|
simprl |
|
16 |
|
simpl3l |
|
17 |
|
simpl2r |
|
18 |
|
axsegcon |
|
19 |
13 14 15 16 17 18
|
syl122anc |
|
20 |
|
simprr |
|
21 |
|
simpl3r |
|
22 |
|
axsegcon |
|
23 |
13 14 20 21 17 22
|
syl122anc |
|
24 |
19 23
|
jca |
|
25 |
24
|
adantr |
|
26 |
|
reeanv |
|
27 |
25 26
|
sylibr |
|
28 |
13 14 17
|
3jca |
|
29 |
28
|
adantr |
|
30 |
16 21 15
|
3jca |
|
31 |
30
|
adantr |
|
32 |
|
simplrr |
|
33 |
|
simprl |
|
34 |
|
simprr |
|
35 |
32 33 34
|
3jca |
|
36 |
29 31 35
|
3jca |
|
37 |
|
simpll |
|
38 |
|
simplr |
|
39 |
|
simpr |
|
40 |
37 38 39
|
3jca |
|
41 |
|
btwnconn1lem2 |
|
42 |
36 40 41
|
syl2an |
|
43 |
|
opeq2 |
|
44 |
43
|
breq2d |
|
45 |
|
opeq2 |
|
46 |
45
|
breq1d |
|
47 |
44 46
|
anbi12d |
|
48 |
47
|
anbi2d |
|
49 |
48
|
anbi2d |
|
50 |
49
|
biimpac |
|
51 |
32 33
|
jca |
|
52 |
29 31 51
|
jca32 |
|
53 |
|
simpll |
|
54 |
|
simplr |
|
55 |
|
simpr |
|
56 |
53 54 55
|
3jca |
|
57 |
|
btwnconn1lem13 |
|
58 |
52 56 57
|
syl2an |
|
59 |
58
|
ex |
|
60 |
50 59
|
syl5 |
|
61 |
60
|
expdimp |
|
62 |
42 61
|
mpd |
|
63 |
62
|
an4s |
|
64 |
63
|
exp32 |
|
65 |
64
|
rexlimdvv |
|
66 |
27 65
|
mpd |
|
67 |
|
orcom |
|
68 |
|
simprrl |
|
69 |
68
|
adantl |
|
70 |
|
opeq2 |
|
71 |
70
|
breq2d |
|
72 |
69 71
|
syl5ibrcom |
|
73 |
|
simprll |
|
74 |
73
|
adantl |
|
75 |
|
opeq2 |
|
76 |
75
|
breq2d |
|
77 |
74 76
|
syl5ibrcom |
|
78 |
72 77
|
orim12d |
|
79 |
67 78
|
syl5bi |
|
80 |
66 79
|
mpd |
|
81 |
80
|
an4s |
|
82 |
81
|
exp32 |
|
83 |
82
|
rexlimdvv |
|
84 |
12 83
|
mpd |
|