Description: A sufficient condition for " F being a real-valued measurable function w.r.t. to the sigma-algebra S ". (Contributed by Glauco Siliprandi, 26-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | issmfd.a | |
|
issmfd.s | |
||
issmfd.d | |
||
issmfd.f | |
||
issmfd.p | |
||
Assertion | issmfd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | issmfd.a | |
|
2 | issmfd.s | |
|
3 | issmfd.d | |
|
4 | issmfd.f | |
|
5 | issmfd.p | |
|
6 | 4 | fdmd | |
7 | 6 3 | eqsstrd | |
8 | 4 | ffdmd | |
9 | 6 | rabeqdv | |
10 | 6 | oveq2d | |
11 | 9 10 | eleq12d | |
12 | 11 | adantr | |
13 | 5 12 | mpbird | |
14 | 13 | ex | |
15 | 1 14 | ralrimi | |
16 | 7 8 15 | 3jca | |
17 | eqid | |
|
18 | 2 17 | issmf | |
19 | 16 18 | mpbird | |