Theorem elelpwi

Description: If A belongs to a part of C , then A belongs to C . (Contributed by FL, 3-Aug-2009)

	Ref	Expression
Assertion	elelpwi	$$⊢\left(A\in B\wedge B\in 𝒫C\right)\to A\in C$$

Proof

Step	Hyp	Ref	Expression
1		elpwi	$$⊢B\in 𝒫C\to B\subseteq C$$
2	1	sseld	$$⊢B\in 𝒫C\to \left(A\in B\to A\in C\right)$$
3	2	impcom	$$⊢\left(A\in B\wedge B\in 𝒫C\right)\to A\in C$$