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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 
|- F/_ x A
Assertion nfpw 
|- F/_ x ~P A

Proof

Step Hyp Ref Expression
1 nfpw.1 
 |-  F/_ x A
2 df-pw 
 |-  ~P A = { y | y C_ A }
3 nfcv 
 |-  F/_ x y
4 3 1 nfss 
 |-  F/ x y C_ A
5 4 nfab 
 |-  F/_ x { y | y C_ A }
6 2 5 nfcxfr 
 |-  F/_ x ~P A