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Metamath Proof Explorer

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