Step |
Hyp |
Ref |
Expression |
1 |
|
4at.l |
|
2 |
|
4at.j |
|
3 |
|
4at.a |
|
4 |
|
3anass |
|
5 |
|
simpl11 |
|
6 |
5
|
hllatd |
|
7 |
|
simpl2l |
|
8 |
|
eqid |
|
9 |
8 3
|
atbase |
|
10 |
7 9
|
syl |
|
11 |
|
simpl2r |
|
12 |
8 3
|
atbase |
|
13 |
11 12
|
syl |
|
14 |
|
simpl12 |
|
15 |
|
simpl31 |
|
16 |
8 2 3
|
hlatjcl |
|
17 |
5 14 15 16
|
syl3anc |
|
18 |
|
simpl32 |
|
19 |
|
simpl33 |
|
20 |
8 2 3
|
hlatjcl |
|
21 |
5 18 19 20
|
syl3anc |
|
22 |
8 2
|
latjcl |
|
23 |
6 17 21 22
|
syl3anc |
|
24 |
8 1 2
|
latjle12 |
|
25 |
6 10 13 23 24
|
syl13anc |
|
26 |
25
|
anbi2d |
|
27 |
4 26
|
syl5bb |
|
28 |
|
simpl13 |
|
29 |
8 3
|
atbase |
|
30 |
28 29
|
syl |
|
31 |
8 2 3
|
hlatjcl |
|
32 |
5 7 11 31
|
syl3anc |
|
33 |
8 1 2
|
latjle12 |
|
34 |
6 30 32 23 33
|
syl13anc |
|
35 |
27 34
|
bitrd |
|
36 |
|
simpl1 |
|
37 |
|
simpl2 |
|
38 |
18 19
|
jca |
|
39 |
|
simpr |
|
40 |
1 2 3
|
4atlem3a |
|
41 |
36 37 38 39 40
|
syl31anc |
|
42 |
|
simp1l |
|
43 |
|
simp1r |
|
44 |
|
simp2 |
|
45 |
|
simp3 |
|
46 |
1 2 3
|
4atlem11b |
|
47 |
42 43 44 45 46
|
syl121anc |
|
48 |
47
|
3exp |
|
49 |
5
|
3ad2ant1 |
|
50 |
14
|
3ad2ant1 |
|
51 |
28
|
3ad2ant1 |
|
52 |
7
|
3ad2ant1 |
|
53 |
11
|
3ad2ant1 |
|
54 |
2 3
|
hlatj4 |
|
55 |
49 50 51 52 53 54
|
syl122anc |
|
56 |
49 50 52
|
3jca |
|
57 |
51 53
|
jca |
|
58 |
|
simp1l3 |
|
59 |
|
simp1r2 |
|
60 |
1 2 3
|
4atlem0be |
|
61 |
49 50 51 52 59 60
|
syl131anc |
|
62 |
|
simp1r1 |
|
63 |
1 2 3
|
4atlem0ae |
|
64 |
49 50 51 52 62 59 63
|
syl132anc |
|
65 |
|
simp1r3 |
|
66 |
2 3
|
hlatj32 |
|
67 |
49 50 51 52 66
|
syl13anc |
|
68 |
67
|
breq2d |
|
69 |
65 68
|
mtbid |
|
70 |
61 64 69
|
3jca |
|
71 |
|
simp2 |
|
72 |
|
simp32 |
|
73 |
|
simp31 |
|
74 |
|
simp33 |
|
75 |
1 2 3
|
4atlem11b |
|
76 |
56 57 58 70 71 72 73 74 75
|
syl323anc |
|
77 |
55 76
|
eqtrd |
|
78 |
77
|
3exp |
|
79 |
8 3
|
atbase |
|
80 |
14 79
|
syl |
|
81 |
8 2
|
latj4rot |
|
82 |
6 80 30 10 13 81
|
syl122anc |
|
83 |
2 3
|
hlatjcom |
|
84 |
5 11 14 83
|
syl3anc |
|
85 |
84
|
oveq1d |
|
86 |
82 85
|
eqtrd |
|
87 |
86
|
3ad2ant1 |
|
88 |
5 14 11
|
3jca |
|
89 |
28 7
|
jca |
|
90 |
|
simpl3 |
|
91 |
88 89 90
|
3jca |
|
92 |
91
|
3ad2ant1 |
|
93 |
1 2 3
|
4noncolr1 |
|
94 |
36 37 39 93
|
syl3anc |
|
95 |
|
necom |
|
96 |
95
|
a1i |
|
97 |
84
|
breq2d |
|
98 |
97
|
notbid |
|
99 |
84
|
oveq1d |
|
100 |
99
|
breq2d |
|
101 |
100
|
notbid |
|
102 |
96 98 101
|
3anbi123d |
|
103 |
94 102
|
mpbid |
|
104 |
103
|
3ad2ant1 |
|
105 |
|
simp2 |
|
106 |
|
simpr3 |
|
107 |
|
simpr1 |
|
108 |
|
simpr2 |
|
109 |
106 107 108
|
3jca |
|
110 |
109
|
3adant2 |
|
111 |
1 2 3
|
4atlem11b |
|
112 |
92 104 105 110 111
|
syl121anc |
|
113 |
87 112
|
eqtrd |
|
114 |
113
|
3exp |
|
115 |
48 78 114
|
3jaod |
|
116 |
41 115
|
mpd |
|
117 |
35 116
|
sylbird |
|