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	$$⊢\left(A\in V\wedge B\in A\right)\to B\in 𝛔\left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		sssigagen	$$⊢A\in V\to A\subseteq 𝛔\left(A\right)$$
2	1	sselda	$$⊢\left(A\in V\wedge B\in A\right)\to B\in 𝛔\left(A\right)$$