ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfrab1 GIF version

Theorem nfrab1 2546
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 2368 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 nfab1 2230 . 2 𝑥{𝑥 ∣ (𝑥𝐴𝜑)}
31, 2nfcxfr 2225 1 𝑥{𝑥𝐴𝜑}
Colors of variables: wff set class
Syntax hints:  wa 102  wcel 1438  {cab 2074  wnfc 2215  {crab 2363
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rab 2368
This theorem is referenced by:  repizf2  3989  rabxfrd  4282  onintrab2im  4325  tfis  4388  fvmptssdm  5371  infssuzcldc  11040
  Copyright terms: Public domain W3C validator