Theorem nfrab1 2649

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 2457	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2314	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2309	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 103   e. wcel 2141   {cab 2156   F/_wnfc 2299   {crab 2452

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rab 2457

This theorem is referenced by:  repizf2  4148  rabxfrd  4454  onintrab2im  4502  tfis  4567  fvmptssdm  5580  infssuzcldc  11906  nnwosdc  11994  imasnopn  13093