Step |
Hyp |
Ref |
Expression |
1 |
|
eldprdi.0 |
|
2 |
|
eldprdi.w |
|
3 |
|
eldprdi.1 |
|
4 |
|
eldprdi.2 |
|
5 |
|
eldprdi.3 |
|
6 |
|
eqid |
|
7 |
2 3 4 5 6
|
dprdff |
|
8 |
7
|
feqmptd |
|
9 |
8
|
adantr |
|
10 |
2 3 4 5
|
dprdfcl |
|
11 |
10
|
adantlr |
|
12 |
3
|
ad2antrr |
|
13 |
4
|
ad2antrr |
|
14 |
|
simpr |
|
15 |
|
eqid |
|
16 |
1 2 12 13 14 11 15
|
dprdfid |
|
17 |
16
|
simpld |
|
18 |
5
|
ad2antrr |
|
19 |
|
eqid |
|
20 |
1 2 12 13 17 18 19
|
dprdfsub |
|
21 |
20
|
simprd |
|
22 |
3 4
|
dprddomcld |
|
23 |
22
|
ad2antrr |
|
24 |
|
fvex |
|
25 |
1
|
fvexi |
|
26 |
24 25
|
ifex |
|
27 |
26
|
a1i |
|
28 |
|
fvexd |
|
29 |
|
eqidd |
|
30 |
7
|
ad2antrr |
|
31 |
30
|
feqmptd |
|
32 |
23 27 28 29 31
|
offval2 |
|
33 |
32
|
oveq2d |
|
34 |
16
|
simprd |
|
35 |
|
simplr |
|
36 |
34 35
|
oveq12d |
|
37 |
|
dprdgrp |
|
38 |
12 37
|
syl |
|
39 |
30 14
|
ffvelrnd |
|
40 |
6 1 19
|
grpsubid1 |
|
41 |
38 39 40
|
syl2anc |
|
42 |
36 41
|
eqtrd |
|
43 |
21 33 42
|
3eqtr3d |
|
44 |
|
eqid |
|
45 |
|
grpmnd |
|
46 |
3 37 45
|
3syl |
|
47 |
46
|
ad2antrr |
|
48 |
6
|
subgacs |
|
49 |
|
acsmre |
|
50 |
38 48 49
|
3syl |
|
51 |
|
imassrn |
|
52 |
3 4
|
dprdf2 |
|
53 |
52
|
ad2antrr |
|
54 |
53
|
frnd |
|
55 |
|
mresspw |
|
56 |
50 55
|
syl |
|
57 |
54 56
|
sstrd |
|
58 |
51 57
|
sstrid |
|
59 |
|
sspwuni |
|
60 |
58 59
|
sylib |
|
61 |
|
eqid |
|
62 |
61
|
mrccl |
|
63 |
50 60 62
|
syl2anc |
|
64 |
|
subgsubm |
|
65 |
63 64
|
syl |
|
66 |
|
oveq1 |
|
67 |
66
|
eleq1d |
|
68 |
|
oveq1 |
|
69 |
68
|
eleq1d |
|
70 |
|
simpr |
|
71 |
70
|
fveq2d |
|
72 |
71
|
oveq2d |
|
73 |
6 1 19
|
grpsubid |
|
74 |
38 39 73
|
syl2anc |
|
75 |
1
|
subg0cl |
|
76 |
63 75
|
syl |
|
77 |
74 76
|
eqeltrd |
|
78 |
77
|
ad2antrr |
|
79 |
72 78
|
eqeltrd |
|
80 |
63
|
ad2antrr |
|
81 |
80 75
|
syl |
|
82 |
50 61 60
|
mrcssidd |
|
83 |
82
|
ad2antrr |
|
84 |
2 12 13 18
|
dprdfcl |
|
85 |
84
|
adantr |
|
86 |
53
|
ffnd |
|
87 |
86
|
ad2antrr |
|
88 |
|
difssd |
|
89 |
|
df-ne |
|
90 |
|
eldifsn |
|
91 |
90
|
biimpri |
|
92 |
89 91
|
sylan2br |
|
93 |
92
|
adantll |
|
94 |
|
fnfvima |
|
95 |
87 88 93 94
|
syl3anc |
|
96 |
|
elunii |
|
97 |
85 95 96
|
syl2anc |
|
98 |
83 97
|
sseldd |
|
99 |
19
|
subgsubcl |
|
100 |
80 81 98 99
|
syl3anc |
|
101 |
67 69 79 100
|
ifbothda |
|
102 |
101
|
fmpttd |
|
103 |
20
|
simpld |
|
104 |
32 103
|
eqeltrrd |
|
105 |
2 12 13 104 44
|
dprdfcntz |
|
106 |
2 12 13 104
|
dprdffsupp |
|
107 |
1 44 47 23 65 102 105 106
|
gsumzsubmcl |
|
108 |
43 107
|
eqeltrrd |
|
109 |
11 108
|
elind |
|
110 |
12 13 14 1 61
|
dprddisj |
|
111 |
109 110
|
eleqtrd |
|
112 |
|
elsni |
|
113 |
111 112
|
syl |
|
114 |
113
|
mpteq2dva |
|
115 |
9 114
|
eqtrd |
|
116 |
115
|
ex |
|
117 |
1
|
gsumz |
|
118 |
46 22 117
|
syl2anc |
|
119 |
|
oveq2 |
|
120 |
119
|
eqeq1d |
|
121 |
118 120
|
syl5ibrcom |
|
122 |
116 121
|
impbid |
|