Step |
Hyp |
Ref |
Expression |
1 |
|
dprdsplit.2 |
|
2 |
|
dprdsplit.i |
|
3 |
|
dprdsplit.u |
|
4 |
|
dprdsplit.s |
|
5 |
|
dprdsplit.1 |
|
6 |
1
|
fdmd |
|
7 |
|
ssun1 |
|
8 |
7 3
|
sseqtrrid |
|
9 |
5 6 8
|
dprdres |
|
10 |
9
|
simpld |
|
11 |
|
dprdsubg |
|
12 |
10 11
|
syl |
|
13 |
|
ssun2 |
|
14 |
13 3
|
sseqtrrid |
|
15 |
5 6 14
|
dprdres |
|
16 |
15
|
simpld |
|
17 |
|
dprdsubg |
|
18 |
16 17
|
syl |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
1 2 3 19 20
|
dmdprdsplit |
|
22 |
5 21
|
mpbid |
|
23 |
22
|
simp2d |
|
24 |
4 19
|
lsmsubg |
|
25 |
12 18 23 24
|
syl3anc |
|
26 |
3
|
eleq2d |
|
27 |
|
elun |
|
28 |
26 27
|
bitrdi |
|
29 |
28
|
biimpa |
|
30 |
|
fvres |
|
31 |
30
|
adantl |
|
32 |
10
|
adantr |
|
33 |
1 8
|
fssresd |
|
34 |
33
|
fdmd |
|
35 |
34
|
adantr |
|
36 |
|
simpr |
|
37 |
32 35 36
|
dprdub |
|
38 |
31 37
|
eqsstrrd |
|
39 |
4
|
lsmub1 |
|
40 |
12 18 39
|
syl2anc |
|
41 |
40
|
adantr |
|
42 |
38 41
|
sstrd |
|
43 |
|
fvres |
|
44 |
43
|
adantl |
|
45 |
16
|
adantr |
|
46 |
1 14
|
fssresd |
|
47 |
46
|
fdmd |
|
48 |
47
|
adantr |
|
49 |
|
simpr |
|
50 |
45 48 49
|
dprdub |
|
51 |
44 50
|
eqsstrrd |
|
52 |
4
|
lsmub2 |
|
53 |
12 18 52
|
syl2anc |
|
54 |
53
|
adantr |
|
55 |
51 54
|
sstrd |
|
56 |
42 55
|
jaodan |
|
57 |
29 56
|
syldan |
|
58 |
5 6 25 57
|
dprdlub |
|
59 |
9
|
simprd |
|
60 |
15
|
simprd |
|
61 |
|
dprdsubg |
|
62 |
5 61
|
syl |
|
63 |
4
|
lsmlub |
|
64 |
12 18 62 63
|
syl3anc |
|
65 |
59 60 64
|
mpbi2and |
|
66 |
58 65
|
eqssd |
|