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Theorem nfrab1 2636
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 2444 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 nfab1 2301 . 2 𝑥{𝑥 ∣ (𝑥𝐴𝜑)}
31, 2nfcxfr 2296 1 𝑥{𝑥𝐴𝜑}
Colors of variables: wff set class
Syntax hints:  wa 103  wcel 2128  {cab 2143  wnfc 2286  {crab 2439
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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rab 2444
This theorem is referenced by:  repizf2  4125  rabxfrd  4431  onintrab2im  4479  tfis  4544  fvmptssdm  5554  infssuzcldc  11850  imasnopn  12769
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