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Theorem nfpw 4558
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 4544 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2982 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3964 . . 3 𝑥 𝑦𝐴
54nfab 2989 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2980 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2804  wnfc 2966  wss 3940  𝒫 cpw 4542
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-in 3947  df-ss 3956  df-pw 4544
This theorem is referenced by:  esum2d  31238  ldsysgenld  31305  stoweidlem57  42208  sge0iunmptlemre  42563  nfafv2  43283
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