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Metamath Proof Explorer

Theorem elpwi

Description: Subset relation implied by membership in a power class. (Contributed by NM, 17-Feb-2007)

		Ref	Expression
	Assertion	elpwi	$⊢ A \in 𝒫 B \to A \subseteq B$

Step	Hyp	Ref	Expression
1		elpwg	$⊢ A \in 𝒫 B \to (A \in 𝒫 B \leftrightarrow A \subseteq B)$
2	1	ibi	$⊢ A \in 𝒫 B \to A \subseteq B$