Step |
Hyp |
Ref |
Expression |
1 |
|
dihglbc.b |
|
2 |
|
dihglbc.g |
|
3 |
|
dihglbc.h |
|
4 |
|
dihglbc.i |
|
5 |
|
dihglbc.l |
|
6 |
|
dihglbcpre.j |
|
7 |
|
dihglbcpre.m |
|
8 |
|
dihglbcpre.a |
|
9 |
|
dihglbcpre.p |
|
10 |
|
dihglbcpre.t |
|
11 |
|
dihglbcpre.r |
|
12 |
|
dihglbcpre.e |
|
13 |
|
dihglbcpre.f |
|
14 |
3 4
|
dihvalrel |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
simp2r |
|
17 |
|
n0 |
|
18 |
16 17
|
sylib |
|
19 |
|
simpr |
|
20 |
|
simpl1 |
|
21 |
3 4
|
dihvalrel |
|
22 |
20 21
|
syl |
|
23 |
19 22
|
jca |
|
24 |
23
|
ex |
|
25 |
24
|
eximdv |
|
26 |
18 25
|
mpd |
|
27 |
|
df-rex |
|
28 |
26 27
|
sylibr |
|
29 |
|
reliin |
|
30 |
28 29
|
syl |
|
31 |
|
id |
|
32 |
|
simp1 |
|
33 |
|
simp1l |
|
34 |
|
hlclat |
|
35 |
33 34
|
syl |
|
36 |
|
simp2l |
|
37 |
1 2
|
clatglbcl |
|
38 |
35 36 37
|
syl2anc |
|
39 |
|
simp3 |
|
40 |
1 5 6 7 8 3
|
lhpmcvr2 |
|
41 |
32 38 39 40
|
syl12anc |
|
42 |
|
simpl1 |
|
43 |
38
|
adantr |
|
44 |
|
simpl3 |
|
45 |
|
simpr |
|
46 |
|
vex |
|
47 |
|
vex |
|
48 |
1 5 6 7 8 3 9 10 11 12 4 13 46 47
|
dihopelvalc |
|
49 |
42 43 44 45 48
|
syl121anc |
|
50 |
|
simpl2r |
|
51 |
|
r19.28zv |
|
52 |
50 51
|
syl |
|
53 |
|
simp11 |
|
54 |
|
simp12l |
|
55 |
|
simp3 |
|
56 |
54 55
|
sseldd |
|
57 |
|
simp13 |
|
58 |
|
simp11l |
|
59 |
58 34
|
syl |
|
60 |
1 5 2
|
clatglble |
|
61 |
59 54 55 60
|
syl3anc |
|
62 |
58
|
hllatd |
|
63 |
38
|
3ad2ant1 |
|
64 |
|
simp11r |
|
65 |
1 3
|
lhpbase |
|
66 |
64 65
|
syl |
|
67 |
1 5
|
lattr |
|
68 |
62 63 56 66 67
|
syl13anc |
|
69 |
61 68
|
mpand |
|
70 |
57 69
|
mtod |
|
71 |
|
simp2l |
|
72 |
|
simp2ll |
|
73 |
1 8
|
atbase |
|
74 |
72 73
|
syl |
|
75 |
1 7
|
latmcl |
|
76 |
62 63 66 75
|
syl3anc |
|
77 |
1 5 6
|
latlej1 |
|
78 |
62 74 76 77
|
syl3anc |
|
79 |
|
simp2r |
|
80 |
78 79
|
breqtrd |
|
81 |
1 5 62 74 63 56 80 61
|
lattrd |
|
82 |
1 5 6 7 8
|
atmod3i1 |
|
83 |
58 72 56 66 81 82
|
syl131anc |
|
84 |
|
eqid |
|
85 |
5 6 84 8 3
|
lhpjat2 |
|
86 |
53 71 85
|
syl2anc |
|
87 |
86
|
oveq2d |
|
88 |
|
hlol |
|
89 |
58 88
|
syl |
|
90 |
1 7 84
|
olm11 |
|
91 |
89 56 90
|
syl2anc |
|
92 |
83 87 91
|
3eqtrd |
|
93 |
1 5 6 7 8 3 9 10 11 12 4 13 46 47
|
dihopelvalc |
|
94 |
53 56 70 71 92 93
|
syl122anc |
|
95 |
94
|
3expa |
|
96 |
95
|
ralbidva |
|
97 |
|
simp11l |
|
98 |
97 34
|
syl |
|
99 |
|
simp11 |
|
100 |
|
simp3l |
|
101 |
|
simp3r |
|
102 |
5 8 3 9
|
lhpocnel2 |
|
103 |
99 102
|
syl |
|
104 |
|
simp2l |
|
105 |
5 8 3 10 13
|
ltrniotacl |
|
106 |
99 103 104 105
|
syl3anc |
|
107 |
3 10 12
|
tendocl |
|
108 |
99 101 106 107
|
syl3anc |
|
109 |
3 10
|
ltrncnv |
|
110 |
99 108 109
|
syl2anc |
|
111 |
3 10
|
ltrnco |
|
112 |
99 100 110 111
|
syl3anc |
|
113 |
1 3 10 11
|
trlcl |
|
114 |
99 112 113
|
syl2anc |
|
115 |
|
simp12l |
|
116 |
1 5 2
|
clatleglb |
|
117 |
98 114 115 116
|
syl3anc |
|
118 |
117
|
3expa |
|
119 |
118
|
pm5.32da |
|
120 |
52 96 119
|
3bitr4rd |
|
121 |
|
opex |
|
122 |
|
eliin |
|
123 |
121 122
|
ax-mp |
|
124 |
120 123
|
bitr4di |
|
125 |
49 124
|
bitrd |
|
126 |
125
|
exp44 |
|
127 |
126
|
imp4a |
|
128 |
127
|
rexlimdv |
|
129 |
41 128
|
mpd |
|
130 |
129
|
eqrelrdv2 |
|
131 |
15 30 31 130
|
syl21anc |
|