Theorem nfrab1 2688

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

Step	Hyp	Ref	Expression
1		df-rab 2495	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2352	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2347	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2178   {cab 2193   F/_wnfc 2337   {crab 2490

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rab 2495

This theorem is referenced by:  repizf2  4222  rabxfrd  4534  onintrab2im  4584  tfis  4649  fvmptssdm  5687  infssuzcldc  10415  nnwosdc  12475  imasnopn  14886  lfgrnloopen  15839