Step |
Hyp |
Ref |
Expression |
1 |
|
vtxdun.i |
|
2 |
|
vtxdun.j |
|
3 |
|
vtxdun.vg |
|
4 |
|
vtxdun.vh |
|
5 |
|
vtxdun.vu |
|
6 |
|
vtxdun.d |
|
7 |
|
vtxdun.fi |
|
8 |
|
vtxdun.fj |
|
9 |
|
vtxdun.n |
|
10 |
|
vtxdun.u |
|
11 |
|
df-rab |
|
12 |
10
|
dmeqd |
|
13 |
|
dmun |
|
14 |
12 13
|
eqtrdi |
|
15 |
14
|
eleq2d |
|
16 |
|
elun |
|
17 |
15 16
|
syl6bb |
|
18 |
17
|
anbi1d |
|
19 |
|
andir |
|
20 |
18 19
|
syl6bb |
|
21 |
20
|
abbidv |
|
22 |
11 21
|
syl5eq |
|
23 |
|
unab |
|
24 |
23
|
eqcomi |
|
25 |
24
|
a1i |
|
26 |
|
df-rab |
|
27 |
10
|
fveq1d |
|
28 |
27
|
adantr |
|
29 |
7
|
funfnd |
|
30 |
29
|
adantr |
|
31 |
8
|
funfnd |
|
32 |
31
|
adantr |
|
33 |
6
|
anim1i |
|
34 |
|
fvun1 |
|
35 |
30 32 33 34
|
syl3anc |
|
36 |
28 35
|
eqtrd |
|
37 |
36
|
eleq2d |
|
38 |
37
|
rabbidva |
|
39 |
26 38
|
syl5eqr |
|
40 |
|
df-rab |
|
41 |
27
|
adantr |
|
42 |
29
|
adantr |
|
43 |
31
|
adantr |
|
44 |
6
|
anim1i |
|
45 |
|
fvun2 |
|
46 |
42 43 44 45
|
syl3anc |
|
47 |
41 46
|
eqtrd |
|
48 |
47
|
eleq2d |
|
49 |
48
|
rabbidva |
|
50 |
40 49
|
syl5eqr |
|
51 |
39 50
|
uneq12d |
|
52 |
22 25 51
|
3eqtrd |
|
53 |
52
|
fveq2d |
|
54 |
1
|
fvexi |
|
55 |
54
|
dmex |
|
56 |
55
|
rabex |
|
57 |
56
|
a1i |
|
58 |
2
|
fvexi |
|
59 |
58
|
dmex |
|
60 |
59
|
rabex |
|
61 |
60
|
a1i |
|
62 |
|
ssrab2 |
|
63 |
|
ssrab2 |
|
64 |
|
ss2in |
|
65 |
62 63 64
|
mp2an |
|
66 |
65 6
|
sseqtrid |
|
67 |
|
ss0 |
|
68 |
66 67
|
syl |
|
69 |
|
hashunx |
|
70 |
57 61 68 69
|
syl3anc |
|
71 |
53 70
|
eqtrd |
|
72 |
|
df-rab |
|
73 |
17
|
anbi1d |
|
74 |
|
andir |
|
75 |
73 74
|
syl6bb |
|
76 |
75
|
abbidv |
|
77 |
72 76
|
syl5eq |
|
78 |
|
unab |
|
79 |
78
|
eqcomi |
|
80 |
79
|
a1i |
|
81 |
|
df-rab |
|
82 |
36
|
eqeq1d |
|
83 |
82
|
rabbidva |
|
84 |
81 83
|
syl5eqr |
|
85 |
|
df-rab |
|
86 |
47
|
eqeq1d |
|
87 |
86
|
rabbidva |
|
88 |
85 87
|
syl5eqr |
|
89 |
84 88
|
uneq12d |
|
90 |
77 80 89
|
3eqtrd |
|
91 |
90
|
fveq2d |
|
92 |
55
|
rabex |
|
93 |
92
|
a1i |
|
94 |
59
|
rabex |
|
95 |
94
|
a1i |
|
96 |
|
ssrab2 |
|
97 |
|
ssrab2 |
|
98 |
|
ss2in |
|
99 |
96 97 98
|
mp2an |
|
100 |
99 6
|
sseqtrid |
|
101 |
|
ss0 |
|
102 |
100 101
|
syl |
|
103 |
|
hashunx |
|
104 |
93 95 102 103
|
syl3anc |
|
105 |
91 104
|
eqtrd |
|
106 |
71 105
|
oveq12d |
|
107 |
|
hashxnn0 |
|
108 |
57 107
|
syl |
|
109 |
|
hashxnn0 |
|
110 |
61 109
|
syl |
|
111 |
|
hashxnn0 |
|
112 |
93 111
|
syl |
|
113 |
|
hashxnn0 |
|
114 |
95 113
|
syl |
|
115 |
108 110 112 114
|
xnn0add4d |
|
116 |
106 115
|
eqtrd |
|
117 |
9 5
|
eleqtrrd |
|
118 |
|
eqid |
|
119 |
|
eqid |
|
120 |
|
eqid |
|
121 |
118 119 120
|
vtxdgval |
|
122 |
117 121
|
syl |
|
123 |
|
eqid |
|
124 |
3 1 123
|
vtxdgval |
|
125 |
9 124
|
syl |
|
126 |
9 4
|
eleqtrrd |
|
127 |
|
eqid |
|
128 |
|
eqid |
|
129 |
127 2 128
|
vtxdgval |
|
130 |
126 129
|
syl |
|
131 |
125 130
|
oveq12d |
|
132 |
116 122 131
|
3eqtr4d |
|