Theorem elpwi

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

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

Proof

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