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Theorem nfrab1 2506
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 2332 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 nfab1 2196 . 2 𝑥{𝑥 ∣ (𝑥𝐴𝜑)}
31, 2nfcxfr 2191 1 𝑥{𝑥𝐴𝜑}
Colors of variables: wff set class
Syntax hints:  wa 101  wcel 1409  {cab 2042  wnfc 2181  {crab 2327
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332
This theorem is referenced by:  repizf2  3943  rabxfrd  4229  onintrab2im  4272  tfis  4334  fvmptssdm  5283
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