| 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 |
|