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Metamath Proof Explorer

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	$⊢ (A \in B \land B \in 𝒫 C) \to A \in C$

Step	Hyp	Ref	Expression
1		elpwi	$⊢ B \in 𝒫 C \to B \subseteq C$
2	1	sseld	$⊢ B \in 𝒫 C \to (A \in B \to A \in C)$
3	2	impcom	$⊢ (A \in B \land B \in 𝒫 C) \to A \in C$