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Theorem nfpw 4624
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 4607 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2903 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3988 . . 3 𝑥 𝑦𝐴
54nfab 2909 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2901 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2712  wnfc 2888  wss 3963  𝒫 cpw 4605
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-ss 3980  df-pw 4607
This theorem is referenced by:  esum2d  34074  ldsysgenld  34141  stoweidlem57  46013  sge0iunmptlemre  46371  nfafv2  47168
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