| Step |
Hyp |
Ref |
Expression |
| 1 |
|
gsumwun.p |
|
| 2 |
|
gsumwun.m |
|
| 3 |
|
gsumwun.e |
|
| 4 |
|
gsumwun.f |
|
| 5 |
|
gsumwun.w |
|
| 6 |
|
oveq2 |
|
| 7 |
6
|
eqeq1d |
|
| 8 |
7
|
2rexbidv |
|
| 9 |
8
|
imbi2d |
|
| 10 |
|
oveq2 |
|
| 11 |
10
|
eqeq1d |
|
| 12 |
11
|
2rexbidv |
|
| 13 |
12
|
imbi2d |
|
| 14 |
|
oveq1 |
|
| 15 |
14
|
eqeq2d |
|
| 16 |
|
oveq2 |
|
| 17 |
16
|
eqeq2d |
|
| 18 |
15 17
|
cbvrex2vw |
|
| 19 |
|
oveq2 |
|
| 20 |
19
|
eqeq1d |
|
| 21 |
20
|
2rexbidv |
|
| 22 |
18 21
|
bitrid |
|
| 23 |
22
|
imbi2d |
|
| 24 |
|
oveq2 |
|
| 25 |
24
|
eqeq1d |
|
| 26 |
25
|
2rexbidv |
|
| 27 |
26
|
imbi2d |
|
| 28 |
|
oveq1 |
|
| 29 |
28
|
eqeq2d |
|
| 30 |
|
oveq2 |
|
| 31 |
30
|
eqeq2d |
|
| 32 |
|
eqid |
|
| 33 |
32
|
subm0cl |
|
| 34 |
3 33
|
syl |
|
| 35 |
32
|
subm0cl |
|
| 36 |
4 35
|
syl |
|
| 37 |
32
|
gsum0 |
|
| 38 |
2
|
cmnmndd |
|
| 39 |
|
eqid |
|
| 40 |
39 32
|
mndidcl |
|
| 41 |
39 1 32
|
mndlid |
|
| 42 |
38 40 41
|
syl2anc2 |
|
| 43 |
37 42
|
eqtr4id |
|
| 44 |
29 31 34 36 43
|
2rspcedvdw |
|
| 45 |
|
oveq1 |
|
| 46 |
45
|
eqeq2d |
|
| 47 |
|
oveq2 |
|
| 48 |
47
|
eqeq2d |
|
| 49 |
3
|
ad6antr |
|
| 50 |
|
simp-4r |
|
| 51 |
|
simpr |
|
| 52 |
1 49 50 51
|
submcld |
|
| 53 |
|
simpllr |
|
| 54 |
38
|
ad5antr |
|
| 55 |
39
|
submss |
|
| 56 |
3 55
|
syl |
|
| 57 |
39
|
submss |
|
| 58 |
4 57
|
syl |
|
| 59 |
56 58
|
unssd |
|
| 60 |
|
sswrd |
|
| 61 |
59 60
|
syl |
|
| 62 |
61
|
sselda |
|
| 63 |
62
|
ad4antr |
|
| 64 |
59
|
adantr |
|
| 65 |
64
|
sselda |
|
| 66 |
65
|
ad3antrrr |
|
| 67 |
39 1
|
gsumccatsn |
|
| 68 |
54 63 66 67
|
syl3anc |
|
| 69 |
|
simpr |
|
| 70 |
69
|
oveq1d |
|
| 71 |
56
|
ad2antrr |
|
| 72 |
71
|
sselda |
|
| 73 |
72
|
ad2antrr |
|
| 74 |
58
|
ad3antrrr |
|
| 75 |
74
|
sselda |
|
| 76 |
75
|
adantr |
|
| 77 |
2
|
ad5antr |
|
| 78 |
39 1
|
cmncom |
|
| 79 |
77 76 66 78
|
syl3anc |
|
| 80 |
39 1 54 73 76 66 79
|
mnd32g |
|
| 81 |
68 70 80
|
3eqtrd |
|
| 82 |
81
|
adantr |
|
| 83 |
46 48 52 53 82
|
2rspcedvdw |
|
| 84 |
|
oveq1 |
|
| 85 |
84
|
eqeq2d |
|
| 86 |
|
oveq2 |
|
| 87 |
86
|
eqeq2d |
|
| 88 |
|
simp-4r |
|
| 89 |
4
|
ad6antr |
|
| 90 |
|
simpllr |
|
| 91 |
|
simpr |
|
| 92 |
1 89 90 91
|
submcld |
|
| 93 |
39 1 54 73 76 66
|
mndassd |
|
| 94 |
68 70 93
|
3eqtrd |
|
| 95 |
94
|
adantr |
|
| 96 |
85 87 88 92 95
|
2rspcedvdw |
|
| 97 |
|
elun |
|
| 98 |
97
|
biimpi |
|
| 99 |
98
|
ad4antlr |
|
| 100 |
83 96 99
|
mpjaodan |
|
| 101 |
100
|
r19.29ffa |
|
| 102 |
101
|
ex |
|
| 103 |
102
|
expl |
|
| 104 |
103
|
com12 |
|
| 105 |
104
|
a2d |
|
| 106 |
9 13 23 27 44 105
|
wrdind |
|
| 107 |
5 106
|
mpcom |
|