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Theorem nfpw 4577
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 4560 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2905 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3934 . . 3 𝑥 𝑦𝐴
54nfab 2911 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2903 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2713  wnfc 2885  wss 3908  𝒫 cpw 4558
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2887  df-ral 3063  df-v 3445  df-in 3915  df-ss 3925  df-pw 4560
This theorem is referenced by:  esum2d  32520  ldsysgenld  32587  stoweidlem57  44193  sge0iunmptlemre  44551  nfafv2  45345
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