Theorem nfpw

Description: Bound-variable hypothesis builder for power class. (Contributed by NM, 28-Oct-2003) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypothesis	nfpw.1	⊢ Ⅎ 𝑥 𝐴
Assertion	nfpw	⊢ Ⅎ 𝑥 𝒫 𝐴

Proof

Step	Hyp	Ref	Expression
1		nfpw.1	⊢ Ⅎ 𝑥 𝐴
2		df-pw	⊢ 𝒫 𝐴 = { 𝑦 ∣ 𝑦 ⊆ 𝐴 }
3		nfcv	⊢ Ⅎ 𝑥 𝑦
4	3 1	nfss	⊢ Ⅎ 𝑥 𝑦 ⊆ 𝐴
5	4	nfab	⊢ Ⅎ 𝑥 { 𝑦 ∣ 𝑦 ⊆ 𝐴 }
6	2 5	nfcxfr	⊢ Ⅎ 𝑥 𝒫 𝐴