Step |
Hyp |
Ref |
Expression |
1 |
|
esumpr.1 |
|
2 |
|
esumpr.2 |
|
3 |
|
esumpr.3 |
|
4 |
|
esumpr.4 |
|
5 |
|
esumpr.5 |
|
6 |
|
esumpr.6 |
|
7 |
|
esumpr2.1 |
|
8 |
|
simpr |
|
9 |
|
dfsn2 |
|
10 |
|
preq2 |
|
11 |
9 10
|
syl5req |
|
12 |
|
esumeq1 |
|
13 |
8 11 12
|
3syl |
|
14 |
1 3 5
|
esumsn |
|
15 |
14
|
adantr |
|
16 |
13 15
|
eqtrd |
|
17 |
|
oveq2 |
|
18 |
|
0xr |
|
19 |
|
eleq1 |
|
20 |
18 19
|
mpbiri |
|
21 |
|
xaddid1 |
|
22 |
20 21
|
syl |
|
23 |
17 22
|
eqtrd |
|
24 |
|
pnfxr |
|
25 |
|
eleq1 |
|
26 |
24 25
|
mpbiri |
|
27 |
|
pnfnemnf |
|
28 |
|
neeq1 |
|
29 |
27 28
|
mpbiri |
|
30 |
|
xaddpnf1 |
|
31 |
26 29 30
|
syl2anc |
|
32 |
|
oveq2 |
|
33 |
|
id |
|
34 |
31 32 33
|
3eqtr4d |
|
35 |
23 34
|
jaoi |
|
36 |
7 35
|
syl6 |
|
37 |
36
|
imp |
|
38 |
|
simpll |
|
39 |
|
eqeq2 |
|
40 |
39
|
biimprd |
|
41 |
8 40
|
syl |
|
42 |
41
|
imp |
|
43 |
38 42 1
|
syl2anc |
|
44 |
4
|
adantr |
|
45 |
5
|
adantr |
|
46 |
43 44 45
|
esumsn |
|
47 |
2 4 6
|
esumsn |
|
48 |
47
|
adantr |
|
49 |
46 48
|
eqtr3d |
|
50 |
49
|
oveq2d |
|
51 |
16 37 50
|
3eqtr2d |
|
52 |
1
|
adantlr |
|
53 |
2
|
adantlr |
|
54 |
3
|
adantr |
|
55 |
4
|
adantr |
|
56 |
5
|
adantr |
|
57 |
6
|
adantr |
|
58 |
|
simpr |
|
59 |
52 53 54 55 56 57 58
|
esumpr |
|
60 |
51 59
|
pm2.61dane |
|