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Theorem nfpw 4619
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 4602 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2905 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3976 . . 3 𝑥 𝑦𝐴
54nfab 2911 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2903 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2714  wnfc 2890  wss 3951  𝒫 cpw 4600
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-ss 3968  df-pw 4602
This theorem is referenced by:  esum2d  34094  ldsysgenld  34161  stoweidlem57  46072  sge0iunmptlemre  46430  nfafv2  47230
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