Theorem nfrab1 2686

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 2493	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2350	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2345	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2176   {cab 2191   F/_wnfc 2335   {crab 2488

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rab 2493

This theorem is referenced by:  repizf2  4206  rabxfrd  4516  onintrab2im  4566  tfis  4631  fvmptssdm  5664  infssuzcldc  10378  nnwosdc  12360  imasnopn  14771