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Metamath Proof Explorer

Theorem pwidg

Description: A set is an element of its power set. (Contributed by Stefan O'Rear, 1-Feb-2015)

		Ref	Expression
	Assertion	pwidg	$⊢ A \in V \to A \in 𝒫 A$

Step	Hyp	Ref	Expression
1		ssid	$⊢ A \subseteq A$
2		elpwg	$⊢ A \in V \to (A \in 𝒫 A \leftrightarrow A \subseteq A)$
3	1 2	mpbiri	$⊢ A \in V \to A \in 𝒫 A$