Theorem elsigagen

Description: Any element of a set is also an element of the sigma-algebra that set generates. (Contributed by Thierry Arnoux, 27-Mar-2017)

	Ref	Expression
Assertion	elsigagen	⊢ ( ( 𝐴 ∈ 𝑉 ∧ 𝐵 ∈ 𝐴 ) → 𝐵 ∈ ( sigaGen ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		sssigagen	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ⊆ ( sigaGen ‘ 𝐴 ) )
2	1	sselda	⊢ ( ( 𝐴 ∈ 𝑉 ∧ 𝐵 ∈ 𝐴 ) → 𝐵 ∈ ( sigaGen ‘ 𝐴 ) )