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Metamath Proof Explorer

Theorem pwexd

Description: Deduction version of the power set axiom. (Contributed by Glauco Siliprandi, 26-Jun-2021)

		Ref	Expression
	Hypothesis	pwexd.1	$⊢ φ \to A \in V$
	Assertion	pwexd	$⊢ φ \to 𝒫 A \in V$

Step	Hyp	Ref	Expression
1		pwexd.1	$⊢ φ \to A \in V$
2		pwexg	$⊢ A \in V \to 𝒫 A \in V$
3	1 2	syl	$⊢ φ \to 𝒫 A \in V$