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 |
|