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Theorem nfpw 4551
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 4537 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2974 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3957 . . 3 𝑥 𝑦𝐴
54nfab 2981 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2972 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2796  wnfc 2958  wss 3933  𝒫 cpw 4535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-in 3940  df-ss 3949  df-pw 4537
This theorem is referenced by:  esum2d  31251  ldsysgenld  31318  stoweidlem57  42219  sge0iunmptlemre  42574  nfafv2  43294
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