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Theorem nfpw 3363
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  F/_
Assertion
Ref Expression
nfpw  F/_ ~P

Proof of Theorem nfpw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-pw 3353 . 2  ~P  {  | 
C_  }
2 nfcv 2175 . . . 4  F/_
3 nfpw.1 . . . 4  F/_
42, 3nfss 2932 . . 3  F/  C_
54nfab 2179 . 2  F/_ {  |  C_  }
61, 5nfcxfr 2172 1  F/_ ~P
Colors of variables: wff set class
Syntax hints:   {cab 2023   F/_wnfc 2162    C_ wss 2911   ~Pcpw 3351
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-in 2918  df-ss 2925  df-pw 3353
This theorem is referenced by: (None)
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