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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