Step |
Hyp |
Ref |
Expression |
1 |
|
gsumwrd2dccat.1 |
|
2 |
|
gsumwrd2dccat.2 |
|
3 |
|
gsumwrd2dccat.3 |
|
4 |
|
gsumwrd2dccat.4 |
|
5 |
|
gsumwrd2dccat.5 |
|
6 |
|
gsumwrd2dccat.6 |
|
7 |
1
|
fvexi |
|
8 |
7
|
a1i |
|
9 |
8 6
|
ssexd |
|
10 |
|
wrdexg |
|
11 |
9 10
|
syl |
|
12 |
11 11
|
xpexd |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
13 14 15 9
|
gsumwrd2dccatlem |
|
17 |
16
|
simpld |
|
18 |
|
f1ocnv |
|
19 |
17 18
|
syl |
|
20 |
16
|
simprd |
|
21 |
20
|
f1oeq1d |
|
22 |
19 21
|
mpbid |
|
23 |
1 2 5 12 3 4 22
|
gsumf1o |
|
24 |
|
relxp |
|
25 |
24
|
a1i |
|
26 |
25
|
ralrimiva |
|
27 |
|
reliun |
|
28 |
26 27
|
sylibr |
|
29 |
|
1stdm |
|
30 |
28 29
|
sylan |
|
31 |
|
lencl |
|
32 |
31
|
adantl |
|
33 |
|
nn0uz |
|
34 |
32 33
|
eleqtrdi |
|
35 |
|
fzn0 |
|
36 |
34 35
|
sylibr |
|
37 |
36
|
dmdju |
|
38 |
37
|
adantr |
|
39 |
30 38
|
eleqtrd |
|
40 |
|
pfxcl |
|
41 |
39 40
|
syl |
|
42 |
|
swrdcl |
|
43 |
39 42
|
syl |
|
44 |
41 43
|
opelxpd |
|
45 |
|
sneq |
|
46 |
|
fveq2 |
|
47 |
46
|
oveq2d |
|
48 |
45 47
|
xpeq12d |
|
49 |
48
|
cbviunv |
|
50 |
49
|
mpteq1i |
|
51 |
50
|
a1i |
|
52 |
3
|
feqmptd |
|
53 |
|
fveq2 |
|
54 |
44 51 52 53
|
fmptco |
|
55 |
54
|
oveq2d |
|
56 |
|
nfv |
|
57 |
3 44
|
cofmpt |
|
58 |
20 51
|
eqtr2d |
|
59 |
49
|
eqcomi |
|
60 |
59
|
a1i |
|
61 |
|
eqidd |
|
62 |
58 60 61
|
f1oeq123d |
|
63 |
19 62
|
mpbird |
|
64 |
|
f1of1 |
|
65 |
63 64
|
syl |
|
66 |
2
|
fvexi |
|
67 |
66
|
a1i |
|
68 |
3 12
|
fexd |
|
69 |
4 65 67 68
|
fsuppco |
|
70 |
57 69
|
eqbrtrrd |
|
71 |
3
|
adantr |
|
72 |
71 44
|
ffvelcdmd |
|
73 |
72
|
fmpttd |
|
74 |
|
vsnex |
|
75 |
|
ovex |
|
76 |
74 75
|
xpex |
|
77 |
76
|
a1i |
|
78 |
77
|
ralrimiva |
|
79 |
|
iunexg |
|
80 |
11 78 79
|
syl2anc |
|
81 |
56 1 2 28 70 5 73 80
|
gsumfs2d |
|
82 |
23 55 81
|
3eqtrd |
|
83 |
|
eqid |
|
84 |
|
vex |
|
85 |
|
vex |
|
86 |
84 85
|
op1std |
|
87 |
84 85
|
op2ndd |
|
88 |
86 87
|
oveq12d |
|
89 |
86
|
fveq2d |
|
90 |
87 89
|
opeq12d |
|
91 |
86 90
|
oveq12d |
|
92 |
88 91
|
opeq12d |
|
93 |
92
|
fveq2d |
|
94 |
37
|
eleq2d |
|
95 |
94
|
biimpa |
|
96 |
95
|
adantr |
|
97 |
|
ovexd |
|
98 |
|
nfcv |
|
99 |
|
fveq2 |
|
100 |
99
|
oveq2d |
|
101 |
11 97 98 100
|
iunsnima2 |
|
102 |
95 101
|
syldan |
|
103 |
102
|
eleq2d |
|
104 |
103
|
biimpa |
|
105 |
100
|
opeliunxp2 |
|
106 |
96 104 105
|
sylanbrc |
|
107 |
|
fvexd |
|
108 |
83 93 106 107
|
fvmptd3 |
|
109 |
108
|
mpteq2dva |
|
110 |
109
|
oveq2d |
|
111 |
110
|
mpteq2dva |
|
112 |
111
|
oveq2d |
|
113 |
102
|
mpteq1d |
|
114 |
113
|
oveq2d |
|
115 |
37 114
|
mpteq12dva |
|
116 |
115
|
oveq2d |
|
117 |
82 112 116
|
3eqtrd |
|