Metamath Proof Explorer


Theorem sssigagen2

Description: A subset of the generating set is also a subset of the generated sigma-algebra. (Contributed by Thierry Arnoux, 22-Sep-2017)

Ref Expression
Assertion sssigagen2 A V B A B 𝛔 A

Proof

Step Hyp Ref Expression
1 simpr A V B A B A
2 sssigagen A V A 𝛔 A
3 2 adantr A V B A A 𝛔 A
4 1 3 sstrd A V B A B 𝛔 A