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Theorem nfpw 4150
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 4138 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2761 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3581 . . 3 𝑥 𝑦𝐴
54nfab 2765 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2759 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2607  wnfc 2748  wss 3560  𝒫 cpw 4136
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2913  df-in 3567  df-ss 3574  df-pw 4138
This theorem is referenced by:  esum2d  29978  ldsysgenld  30046  stoweidlem57  39611  sge0iunmptlemre  39969
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