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Theorem nfrab1 2670
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 2477 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 nfab1 2334 . 2 𝑥{𝑥 ∣ (𝑥𝐴𝜑)}
31, 2nfcxfr 2329 1 𝑥{𝑥𝐴𝜑}
Colors of variables: wff set class
Syntax hints:  wa 104  wcel 2160  {cab 2175  wnfc 2319  {crab 2472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rab 2477
This theorem is referenced by:  repizf2  4180  rabxfrd  4487  onintrab2im  4535  tfis  4600  fvmptssdm  5621  infssuzcldc  11987  nnwosdc  12075  imasnopn  14276
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