Step |
Hyp |
Ref |
Expression |
1 |
|
dvdsmulf1o.1 |
|
2 |
|
dvdsmulf1o.2 |
|
3 |
|
dvdsmulf1o.3 |
|
4 |
|
dvdsmulf1o.x |
|
5 |
|
dvdsmulf1o.y |
|
6 |
|
dvdsmulf1o.z |
|
7 |
|
fsumdvdsmul.4 |
|
8 |
|
fsumdvdsmul.5 |
|
9 |
|
fsumdvdsmul.6 |
|
10 |
|
fsumdvdsmul.7 |
|
11 |
|
fzfid |
|
12 |
|
dvdsssfz1 |
|
13 |
1 12
|
syl |
|
14 |
4 13
|
eqsstrid |
|
15 |
11 14
|
ssfid |
|
16 |
|
fzfid |
|
17 |
|
dvdsssfz1 |
|
18 |
2 17
|
syl |
|
19 |
5 18
|
eqsstrid |
|
20 |
16 19
|
ssfid |
|
21 |
20 8
|
fsumcl |
|
22 |
15 21 7
|
fsummulc1 |
|
23 |
20
|
adantr |
|
24 |
8
|
adantlr |
|
25 |
23 7 24
|
fsummulc2 |
|
26 |
9
|
anassrs |
|
27 |
26
|
sumeq2dv |
|
28 |
25 27
|
eqtrd |
|
29 |
28
|
sumeq2dv |
|
30 |
|
fveq2 |
|
31 |
|
df-ov |
|
32 |
30 31
|
eqtr4di |
|
33 |
32
|
csbeq1d |
|
34 |
|
ovex |
|
35 |
34 10
|
csbie |
|
36 |
33 35
|
eqtrdi |
|
37 |
7
|
adantrr |
|
38 |
8
|
adantrl |
|
39 |
37 38
|
mulcld |
|
40 |
9 39
|
eqeltrrd |
|
41 |
36 15 20 40
|
fsumxp |
|
42 |
|
nfcv |
|
43 |
|
nfcsb1v |
|
44 |
|
csbeq1a |
|
45 |
42 43 44
|
cbvsumi |
|
46 |
|
csbeq1 |
|
47 |
|
xpfi |
|
48 |
15 20 47
|
syl2anc |
|
49 |
1 2 3 4 5 6
|
dvdsmulf1o |
|
50 |
|
fvres |
|
51 |
50
|
adantl |
|
52 |
40
|
ralrimivva |
|
53 |
36
|
eleq1d |
|
54 |
53
|
ralxp |
|
55 |
52 54
|
sylibr |
|
56 |
|
ax-mulf |
|
57 |
|
ffn |
|
58 |
56 57
|
ax-mp |
|
59 |
4
|
ssrab3 |
|
60 |
|
nnsscn |
|
61 |
59 60
|
sstri |
|
62 |
5
|
ssrab3 |
|
63 |
62 60
|
sstri |
|
64 |
|
xpss12 |
|
65 |
61 63 64
|
mp2an |
|
66 |
46
|
eleq1d |
|
67 |
66
|
ralima |
|
68 |
58 65 67
|
mp2an |
|
69 |
|
df-ima |
|
70 |
|
f1ofo |
|
71 |
|
forn |
|
72 |
49 70 71
|
3syl |
|
73 |
69 72
|
syl5eq |
|
74 |
73
|
raleqdv |
|
75 |
68 74
|
bitr3id |
|
76 |
55 75
|
mpbid |
|
77 |
76
|
r19.21bi |
|
78 |
46 48 49 51 77
|
fsumf1o |
|
79 |
45 78
|
syl5eq |
|
80 |
41 79
|
eqtr4d |
|
81 |
22 29 80
|
3eqtrd |
|