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Theorem nfpw 4365
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 4353 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2948 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3791 . . 3 𝑥 𝑦𝐴
54nfab 2953 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2946 1 𝑥𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  {cab 2792  wnfc 2935  wss 3769  𝒫 cpw 4351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-nfc 2937  df-ral 3101  df-in 3776  df-ss 3783  df-pw 4353
This theorem is referenced by:  esum2d  30480  ldsysgenld  30548  stoweidlem57  40753  sge0iunmptlemre  41111  nfafv2  41807
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