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Metamath Proof Explorer

Theorem velpw

Description: Setvar variable membership in a power class. (Contributed by David A. Wheeler, 8-Dec-2018)

		Ref	Expression
	Assertion	velpw	$⊢ x \in 𝒫 A \leftrightarrow x \subseteq A$

Step	Hyp	Ref	Expression
1		vex	$⊢ x \in V$
2	1	elpw	$⊢ x \in 𝒫 A \leftrightarrow x \subseteq A$