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Theorem nfrab1 2538
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 2362 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 nfab1 2225 . 2  |-  F/_ x { x  |  (
x  e.  A  /\  ph ) }
31, 2nfcxfr 2220 1  |-  F/_ x { x  e.  A  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 102    e. wcel 1434   {cab 2069   F/_wnfc 2210   {crab 2357
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362
This theorem is referenced by:  repizf2  3956  rabxfrd  4247  onintrab2im  4290  tfis  4352  fvmptssdm  5308  infssuzcldc  10572
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