Description: Value of the Caratheodory sigma-Algebra construction function. (Contributed by Thierry Arnoux, 17-May-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | carsgval.1 | |
|
carsgval.2 | |
||
Assertion | carsgval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | carsgval.1 | |
|
2 | carsgval.2 | |
|
3 | df-carsg | |
|
4 | simpr | |
|
5 | 4 | dmeqd | |
6 | 2 | fdmd | |
7 | 6 | adantr | |
8 | 5 7 | eqtrd | |
9 | 8 | unieqd | |
10 | unipw | |
|
11 | 9 10 | eqtrdi | |
12 | 11 | pweqd | |
13 | fveq1 | |
|
14 | fveq1 | |
|
15 | 13 14 | oveq12d | |
16 | fveq1 | |
|
17 | 15 16 | eqeq12d | |
18 | 17 | adantl | |
19 | 12 18 | raleqbidv | |
20 | 12 19 | rabeqbidv | |
21 | 1 | pwexd | |
22 | 2 21 | fexd | |
23 | pwexg | |
|
24 | rabexg | |
|
25 | 1 23 24 | 3syl | |
26 | 3 20 22 25 | fvmptd2 | |