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Theorem nfpw 4120
 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 4110 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2751 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3561 . . 3 𝑥 𝑦𝐴
54nfab 2755 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2749 1 𝑥𝒫 𝐴
 Colors of variables: wff setvar class Syntax hints:  {cab 2596  Ⅎwnfc 2738   ⊆ wss 3540  𝒫 cpw 4108 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-in 3547  df-ss 3554  df-pw 4110 This theorem is referenced by:  esum2d  29482  ldsysgenld  29550  stoweidlem57  38950  sge0iunmptlemre  39308
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