Theorem pwexd

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

	Ref	Expression
Hypothesis	pwexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	pwexd	⊢ ( 𝜑 → 𝒫 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		pwexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		pwexg	⊢ ( 𝐴 ∈ 𝑉 → 𝒫 𝐴 ∈ V )
3	1 2	syl	⊢ ( 𝜑 → 𝒫 𝐴 ∈ V )