Step |
Hyp |
Ref |
Expression |
1 |
|
caratheodory.o |
|
2 |
|
caratheodory.s |
|
3 |
1 2
|
caragensal |
|
4 |
|
eqid |
|
5 |
1 4
|
omef |
|
6 |
|
caragenval |
|
7 |
1 6
|
syl |
|
8 |
7
|
eqcomd |
|
9 |
2
|
eqcomi |
|
10 |
9
|
a1i |
|
11 |
8 10
|
eqtr2d |
|
12 |
|
ssrab2 |
|
13 |
11 12
|
eqsstrdi |
|
14 |
5 13
|
fssresd |
|
15 |
1 2
|
caragen0 |
|
16 |
|
fvres |
|
17 |
15 16
|
syl |
|
18 |
1
|
ome0 |
|
19 |
17 18
|
eqtrd |
|
20 |
|
simp1 |
|
21 |
|
simp2 |
|
22 |
|
fveq2 |
|
23 |
22
|
cbvdisjv |
|
24 |
23
|
biimpi |
|
25 |
24
|
3ad2ant3 |
|
26 |
1
|
3ad2ant1 |
|
27 |
|
simp2 |
|
28 |
23
|
biimpri |
|
29 |
28
|
3ad2ant3 |
|
30 |
|
fveq2 |
|
31 |
30
|
cbviunv |
|
32 |
31
|
mpteq2i |
|
33 |
26 4 2 27 29 32
|
caratheodorylem2 |
|
34 |
20 21 25 33
|
syl3anc |
|
35 |
3
|
adantr |
|
36 |
|
nnenom |
|
37 |
|
endom |
|
38 |
36 37
|
ax-mp |
|
39 |
38
|
a1i |
|
40 |
|
ffvelrn |
|
41 |
40
|
adantll |
|
42 |
35 39 41
|
saliuncl |
|
43 |
|
fvres |
|
44 |
42 43
|
syl |
|
45 |
44
|
3adant3 |
|
46 |
|
fvres |
|
47 |
41 46
|
syl |
|
48 |
47
|
mpteq2dva |
|
49 |
48
|
fveq2d |
|
50 |
49
|
3adant3 |
|
51 |
34 45 50
|
3eqtr4d |
|
52 |
3 14 19 51
|
ismeannd |
|