Theorem nfrab1 2533

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 2357	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2221	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2216	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 102   e. wcel 1433   {cab 2067   F/_wnfc 2206   {crab 2352

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 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rab 2357

This theorem is referenced by:  repizf2  3936  rabxfrd  4219  onintrab2im  4262  tfis  4324  fvmptssdm  5276  infssuzcldc  10347