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Theorem nfpw 4583
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 4566 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2904 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3940 . . 3 𝑥 𝑦𝐴
54nfab 2910 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2902 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2710  wnfc 2884  wss 3914  𝒫 cpw 4564
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3062  df-v 3449  df-in 3921  df-ss 3931  df-pw 4566
This theorem is referenced by:  esum2d  32756  ldsysgenld  32823  stoweidlem57  44388  sge0iunmptlemre  44746  nfafv2  45540
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