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Theorem nfpw 4521
 Description: Bound-variable hypothesis builder for power class. (Contributed by NM, 28-Oct-2003.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
nfpw.1 𝑥𝐴
Assertion
Ref Expression
nfpw 𝑥𝒫 𝐴

Proof of Theorem nfpw
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-pw 4502 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2955 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3909 . . 3 𝑥 𝑦𝐴
54nfab 2961 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2953 1 𝑥𝒫 𝐴
 Colors of variables: wff setvar class Syntax hints:  {cab 2776  Ⅎwnfc 2936   ⊆ wss 3883  𝒫 cpw 4500 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-v 3444  df-in 3890  df-ss 3900  df-pw 4502 This theorem is referenced by:  esum2d  31528  ldsysgenld  31595  stoweidlem57  42867  sge0iunmptlemre  43222  nfafv2  43942
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