Theorem pwexr

Description: Converse of the Axiom of Power Sets. Note that it does not require ax-pow . (Contributed by NM, 11-Nov-2003)

	Ref	Expression
Assertion	pwexr	$$⊢𝒫A\in V\to A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		unipw	$$⊢\bigcup 𝒫A=A$$
2		uniexg	$$⊢𝒫A\in V\to \bigcup 𝒫A\in \mathrm{V}$$
3	1 2	eqeltrrid	$$⊢𝒫A\in V\to A\in \mathrm{V}$$