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Theorem nfrab1 2587
Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfrab1 𝑥{𝑥𝐴𝜑}

Proof of Theorem nfrab1
StepHypRef Expression
1 df-rab 2402 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 nfab1 2260 . 2 𝑥{𝑥 ∣ (𝑥𝐴𝜑)}
31, 2nfcxfr 2255 1 𝑥{𝑥𝐴𝜑}
Colors of variables: wff set class
Syntax hints:  wa 103  wcel 1465  {cab 2103  wnfc 2245  {crab 2397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rab 2402
This theorem is referenced by:  repizf2  4056  rabxfrd  4360  onintrab2im  4404  tfis  4467  fvmptssdm  5473  infssuzcldc  11571  imasnopn  12395
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