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Theorem nfrab1 2610
Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfrab1  |-  F/_ x { x  e.  A  |  ph }

Proof of Theorem nfrab1
StepHypRef Expression
1 df-rab 2425 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 nfab1 2283 . 2  |-  F/_ x { x  |  (
x  e.  A  /\  ph ) }
31, 2nfcxfr 2278 1  |-  F/_ x { x  e.  A  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 1480   {cab 2125   F/_wnfc 2268   {crab 2420
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425
This theorem is referenced by:  repizf2  4086  rabxfrd  4390  onintrab2im  4434  tfis  4497  fvmptssdm  5505  infssuzcldc  11651  imasnopn  12478
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