Step |
Hyp |
Ref |
Expression |
1 |
|
carsgval.1 |
|
2 |
|
carsgval.2 |
|
3 |
|
carsgsiga.1 |
|
4 |
|
carsgsiga.2 |
|
5 |
|
simpr |
|
6 |
5
|
uneq2d |
|
7 |
|
unidm |
|
8 |
6 7
|
eqtr3di |
|
9 |
8
|
fveq2d |
|
10 |
|
iccssxr |
|
11 |
|
simp1 |
|
12 |
11 2
|
syl |
|
13 |
|
simp2 |
|
14 |
12 13
|
ffvelrnd |
|
15 |
10 14
|
sselid |
|
16 |
15
|
adantr |
|
17 |
5
|
fveq2d |
|
18 |
17 16
|
eqeltrrd |
|
19 |
|
simp3 |
|
20 |
12 19
|
ffvelrnd |
|
21 |
20
|
adantr |
|
22 |
|
elxrge0 |
|
23 |
22
|
simprbi |
|
24 |
21 23
|
syl |
|
25 |
|
xraddge02 |
|
26 |
25
|
imp |
|
27 |
16 18 24 26
|
syl21anc |
|
28 |
9 27
|
eqbrtrd |
|
29 |
|
uniprg |
|
30 |
29
|
fveq2d |
|
31 |
30
|
3adant1 |
|
32 |
|
prct |
|
33 |
32
|
3adant1 |
|
34 |
|
prssi |
|
35 |
34
|
3adant1 |
|
36 |
|
prex |
|
37 |
|
breq1 |
|
38 |
|
sseq1 |
|
39 |
37 38
|
3anbi23d |
|
40 |
|
unieq |
|
41 |
40
|
fveq2d |
|
42 |
|
esumeq1 |
|
43 |
41 42
|
breq12d |
|
44 |
39 43
|
imbi12d |
|
45 |
44 4
|
vtoclg |
|
46 |
36 45
|
ax-mp |
|
47 |
11 33 35 46
|
syl3anc |
|
48 |
31 47
|
eqbrtrrd |
|
49 |
48
|
adantr |
|
50 |
|
simpr |
|
51 |
50
|
fveq2d |
|
52 |
51
|
adantlr |
|
53 |
|
simpr |
|
54 |
53
|
fveq2d |
|
55 |
54
|
adantlr |
|
56 |
13
|
adantr |
|
57 |
19
|
adantr |
|
58 |
14
|
adantr |
|
59 |
20
|
adantr |
|
60 |
|
simpr |
|
61 |
52 55 56 57 58 59 60
|
esumpr |
|
62 |
49 61
|
breqtrd |
|
63 |
28 62
|
pm2.61dane |
|