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

Theorem nfrab1 2483
 Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfrab1 x{x Aφ}

Proof of Theorem nfrab1
StepHypRef Expression
1 df-rab 2309 . 2 {x Aφ} = {x ∣ (x A φ)}
2 nfab1 2177 . 2 x{x ∣ (x A φ)}
31, 2nfcxfr 2172 1 x{x Aφ}
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ∈ wcel 1390  {cab 2023  Ⅎwnfc 2162  {crab 2304 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309 This theorem is referenced by:  repizf2  3906  rabxfrd  4167  tfis  4249  fvmptssdm  5198
 Copyright terms: Public domain W3C validator